Daily Papers

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to long-horizon LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on two challenging agent benchmarks, ALFWorld and WebShop, using Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals and achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over the GRPO baseline: all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

Reinforcement learning with verifiable rewards has significantly advanced the reasoning capabilities of large language models, yet how to explicitly steer training toward exploration or exploitation remains an open problem. We introduce Token Hidden Reward (THR), a token-level metric that quantifies each token's influence on the likelihood of correct responses under Group Relative Policy Optimization (GRPO). We find that training dynamics are dominated by a small subset of tokens with high absolute THR values. Most interestingly, tokens with positive THR strengthen confidence in correct outputs, thus favoring exploitation, while tokens with negative THR preserve probability mass for alternative outputs, enabling exploration. This insight suggests a natural intervention: a THR-guided reweighting algorithm that modulates GRPO's learning signals to explicitly bias training toward exploitation or exploration. We validate the efficacy of this algorithm on diverse math reasoning benchmarks. By amplifying tokens with positive THR value and weakening negative ones, our algorithm improves greedy-decoding accuracy, favoring exploitation. The reverse strategy yields consistent gains in Pass@K accuracy, favoring exploration. We further demonstrate that our algorithm integrates seamlessly with other RL objectives such as GSPO and generalizes across architectures including Llama. These findings establish THR as a principled and fine-grained mechanism for dynamically controlling exploration and exploitation in RL-tuned LLMs, providing new tools for targeted fine-tuning in reasoning-intensive applications.

Training large language models (LLMs) for complex reasoning via Reinforcement Learning with Verifiable Rewards (RLVR) is effective but limited by reliance on costly, domain-specific supervision. We explore Reinforcement Learning from Internal Feedback (RLIF), a framework that enables LLMs to learn from intrinsic signals without external rewards or labeled data. We propose Intuitor, an RLIF method that uses a model's own confidence, termed self-certainty, as its sole reward signal. Intuitor replaces external rewards in Group Relative Policy Optimization (GRPO) with self-certainty scores, enabling fully unsupervised learning. Experiments demonstrate that Intuitor matches GRPO's performance on mathematical benchmarks while achieving superior generalization to out-of-domain tasks like code generation, without requiring gold solutions or test cases. Our findings show that intrinsic model signals can drive effective learning across domains, offering a scalable alternative to RLVR for autonomous AI systems where verifiable rewards are unavailable. Code is available at https://github.com/sunblaze-ucb/Intuitor

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

DeepSeek-R1-Zero has shown that reinforcement learning (RL) at scale can directly enhance the reasoning capabilities of LLMs without supervised fine-tuning. In this work, we critically examine R1-Zero-like training by analyzing its two core components: base models and RL. We investigate a wide range of base models, including DeepSeek-V3-Base, to understand how pretraining characteristics influence RL performance. Our analysis reveals that DeepSeek-V3-Base already exhibit ''Aha moment'', while Qwen2.5 base models demonstrate strong reasoning capabilities even without prompt templates, suggesting potential pretraining biases. Additionally, we identify an optimization bias in Group Relative Policy Optimization (GRPO), which artificially increases response length (especially for incorrect outputs) during training. To address this, we introduce Dr. GRPO, an unbiased optimization method that improves token efficiency while maintaining reasoning performance. Leveraging these insights, we present a minimalist R1-Zero recipe that achieves 43.3% accuracy on AIME 2024 with a 7B base model, establishing a new state-of-the-art. Our code is available at https://github.com/sail-sg/understand-r1-zero.

We present Skywork R1V2, a next-generation multimodal reasoning model and a major leap forward from its predecessor, Skywork R1V. At its core, R1V2 introduces a hybrid reinforcement learning paradigm that harmonizes reward-model guidance with rule-based strategies, thereby addressing the long-standing challenge of balancing sophisticated reasoning capabilities with broad generalization. To further enhance training efficiency, we propose the Selective Sample Buffer (SSB) mechanism, which effectively counters the ``Vanishing Advantages'' dilemma inherent in Group Relative Policy Optimization (GRPO) by prioritizing high-value samples throughout the optimization process. Notably, we observe that excessive reinforcement signals can induce visual hallucinations--a phenomenon we systematically monitor and mitigate through calibrated reward thresholds throughout the training process. Empirical results affirm the exceptional capability of R1V2, with benchmark-leading performances such as 62.6 on OlympiadBench, 79.0 on AIME2024, 63.6 on LiveCodeBench, and 74.0 on MMMU. These results underscore R1V2's superiority over existing open-source models and demonstrate significant progress in closing the performance gap with premier proprietary systems, including Gemini 2.5 and OpenAI o4-mini. The Skywork R1V2 model weights have been publicly released to promote openness and reproducibility https://huggingface.co/Skywork/Skywork-R1V2-38B.

Large language models (LLMs) have achieved impressive reasoning performance, with reinforcement learning with verifiable rewards (RLVR) emerging as a standard paradigm for post-training. A representative algorithm, group relative policy optimization (GRPO) (Shao et al., 2024), computes advantages by normalizing outcome rewards within response groups, but suffers from a vanishing advantage issue when all responses in a group receive identical rewards. To address this issue, we propose Adaptive Rollout and Response Reuse Policy Optimization (AR3PO), a sampling efficient RLVR algorithm that introduces two novel techniques: adaptive rollout, which dynamically allocates more responses to difficult prompts while saving computation on easier ones, and response reuse, which leverages previously generated correct responses to provide useful training signals. We compare AR3PO with strong RLVR baselines on multiple representative benchmarks using two different families of base models. Across the 7B and 8B models, AR3PO consistently outperforms GRPO and matches or surpasses DAPO (Yu et al., 2025), reducing rollout cost by up to 4.2x. On the larger 32B model, AR3PO achieves comparable performance to DAPO at similar training steps while maintaining substantially lower rollout cost.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12{36} as wrong when compared against the canonical 1{3} due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

Reinforcement learning (RL) has demonstrated significant success in enhancing reasoning capabilities in large language models (LLMs). One of the most widely used RL methods is Group Relative Policy Optimization (GRPO)~Shao-2024-Deepseekmath, known for its memory efficiency and success in training DeepSeek-R1~Guo-2025-Deepseek. However, GRPO stalls when all sampled responses in a group are incorrect -- referred to as an all-negative-sample group -- as it fails to update the policy, hindering learning progress. The contributions of this paper are two-fold. First, we propose a simple yet effective framework that introduces response diversity within all-negative-sample groups in GRPO using AI feedback. We also provide a theoretical analysis, via a stylized model, showing how this diversification improves learning dynamics. Second, we empirically validate our approach, showing the improved performance across various model sizes (7B, 14B, 32B) in both offline and online learning settings with 10 benchmarks, including base and distilled variants. Our findings highlight that learning from all-negative-sample groups is not only feasible but beneficial, advancing recent insights from Xiong-2025-Minimalist.

Despite their remarkable reasoning capabilities across diverse domains, large language models (LLMs) face fundamental challenges in natively functioning as generative reasoning recommendation models (GRRMs), where the intrinsic modeling gap between textual semantics and collaborative filtering signals, combined with the sparsity and stochasticity of user feedback, presents significant obstacles. This work explores how to build GRRMs by adapting pre-trained LLMs, which achieves a unified understanding-reasoning-prediction manner for recommendation tasks. We propose GREAM, an end-to-end framework that integrates three components: (i) Collaborative-Semantic Alignment, which fuses heterogeneous textual evidence to construct semantically consistent, discrete item indices and auxiliary alignment tasks that ground linguistic representations in interaction semantics; (ii) Reasoning Curriculum Activation, which builds a synthetic dataset with explicit Chain-of-Thought supervision and a curriculum that progresses through behavioral evidence extraction, latent preference modeling, intent inference, recommendation formulation, and denoised sequence rewriting; and (iii) Sparse-Regularized Group Policy Optimization (SRPO), which stabilizes post-training via Residual-Sensitive Verifiable Reward and Bonus-Calibrated Group Advantage Estimation, enabling end-to-end optimization under verifiable signals despite sparse successes. GREAM natively supports two complementary inference modes: Direct Sequence Recommendation for high-throughput, low-latency deployment, and Sequential Reasoning Recommendation that first emits an interpretable reasoning chain for causal transparency. Experiments on three datasets demonstrate consistent gains over strong baselines, providing a practical path toward verifiable-RL-driven LLM recommenders.

Post-training plays a crucial role in refining and aligning large language models to meet specific tasks and human preferences. While recent advancements in post-training techniques, such as Group Relative Policy Optimization (GRPO), leverage increased sampling with relative reward scoring to achieve superior performance, these methods often suffer from training instability that limits their practical adoption. To address this challenge, we present Group Variance Policy Optimization (GVPO). GVPO incorporates the analytical solution to KL-constrained reward maximization directly into its gradient weights, ensuring alignment with the optimal policy. The method provides intuitive physical interpretations: its gradient mirrors the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly the KL-constrained reward maximization objective, (2) it supports flexible sampling distributions that avoids on-policy and importance sampling limitations. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training.

Recent advances in Large Language Model (LLM) agents have demonstrated their promising general capabilities. However, their performance in specialized real-world domains often degrades due to challenges in effectively integrating external tools and specific prompting strategies. While methods like agentic reinforcement learning have been proposed to address this, they typically rely on costly parameter updates, for example, through a process that uses Supervised Fine-Tuning (SFT) followed by a Reinforcement Learning (RL) phase with Group Relative Policy Optimization (GRPO) to alter the output distribution. However, we argue that LLMs can achieve a similar effect on the output distribution by learning experiential knowledge as a token prior, which is a far more lightweight approach that not only addresses practical data scarcity but also avoids the common issue of overfitting. To this end, we propose Training-Free Group Relative Policy Optimization (Training-Free GRPO), a cost-effective solution that enhances LLM agent performance without any parameter updates. Our method leverages the group relative semantic advantage instead of numerical ones within each group of rollouts, iteratively distilling high-quality experiential knowledge during multi-epoch learning on a minimal ground-truth data. Such knowledge serves as the learned token prior, which is seamlessly integrated during LLM API calls to guide model behavior. Experiments on mathematical reasoning and web searching tasks demonstrate that Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, significantly improves out-of-domain performance. With just a few dozen training samples, Training-Free GRPO outperforms fine-tuned small LLMs with marginal training data and cost.

Speech Recognition has seen a dramatic shift towards adopting Large Language Models (LLMs). This shift is partly driven by good scalability properties demonstrated by LLMs, ability to leverage large amounts of labelled, unlabelled speech and text data, streaming capabilities with auto-regressive framework and multi-tasking with instruction following characteristics of LLMs. However, simple next-token prediction objective, typically employed with LLMs, have certain limitations in performance and challenges with hallucinations. In this paper, we propose application of Group Relative Policy Optimization (GRPO) to enable reinforcement learning from human feedback for automatic speech recognition (ASR). We design simple rule based reward functions to guide the policy updates. We demonstrate significant improvements in word error rate (upto 18.4% relative), reduction in hallucinations, increased robustness on out-of-domain datasets and effectiveness in domain adaptation.

This paper introduces Group Sequence Policy Optimization (GSPO), our stable, efficient, and performant reinforcement learning algorithm for training large language models. Unlike previous algorithms that adopt token-level importance ratios, GSPO defines the importance ratio based on sequence likelihood and performs sequence-level clipping, rewarding, and optimization. We demonstrate that GSPO achieves superior training efficiency and performance compared to the GRPO algorithm, notably stabilizes Mixture-of-Experts (MoE) RL training, and has the potential for simplifying the design of RL infrastructure. These merits of GSPO have contributed to the remarkable improvements in the latest Qwen3 models.

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

RLVR has enhanced the reasoning capabilities of Large Language Models (LLMs) across various tasks. However, GRPO, a representative RLVR algorithm, suffers from a critical limitation: when all responses within a group are either entirely correct or entirely incorrect, the model fails to learn from these homogeneous responses. This is particularly problematic for homogeneously incorrect groups, where GRPO's advantage function yields a value of zero, leading to null gradients and the loss of valuable learning signals. To overcome this issue, we propose NGRPO (Negative-enhanced Group Relative Policy Optimization), an algorithm designed to convert homogeneous errors into robust learning signals. First, NGRPO introduces Advantage Calibration. This mechanism hypothesizes the existence of a virtual maximum-reward sample during advantage calculation, thereby altering the mean and variance of rewards within a group and ensuring that the advantages for homogeneously incorrect samples are no longer zero. Second, NGRPO employs Asymmetric Clipping, which relaxes the update magnitude for positive samples while imposing stricter constraints on that of negative samples. This serves to stabilize the exploration pressure introduced by the advantage calibration. Our experiments on Qwen2.5-Math-7B demonstrate that NGRPO significantly outperforms baselines such as PPO, GRPO, DAPO, and PSR-NSR on mathematical benchmarks including MATH500, AMC23, and AIME2025. These results validate NGRPO's ability to learn from homogeneous errors, leading to stable and substantial improvements in mathematical reasoning. Our code is available at https://github.com/nangongrui-ngr/NGRPO.

The Retrieval-Augmented Generation (RAG) systems' performance on Thai legal question answering is still limited, especially for questions requiring extensive, complex legal reasoning. To address these limitations, we introduce an approach aligning LLMs toward improved law citation accuracy and better response quality using Group-Relative Policy Optimization (GRPO). Our approach leverages BGE-M3 embeddings as a cost-efficient semantic-similarity reward, significantly reducing computational expenses up to 2.5x compared to large language model judges. Experiments on the NitiBench benchmark demonstrate substantial improvements: GRPO achieves up to 90% citation-F1 gains from the base model and a 31% increase in joint quality metrics over instruction tuning. Crucially, our method shows enhanced robustness on complex legal reasoning tasks compared to instruction tuning, providing an effective and resource-efficient solution for enhancing Thai legal LLMs.

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly enhanced the reasoning abilities of large language models (LLMs). Its success, however, largely depends on strong base models with rich world knowledge, yielding only modest improvements for small-size language models (SLMs). To address this limitation, we investigate Guided GRPO, which injects ground-truth reasoning steps into roll-out trajectories to compensate for SLMs' inherent weaknesses. Through a comprehensive study of various guidance configurations, we find that naively adding guidance delivers limited gains. These insights motivate G^2RPO-A, an adaptive algorithm that automatically adjusts guidance strength in response to the model's evolving training dynamics. Experiments on mathematical reasoning and code-generation benchmarks confirm that G^2RPO-A substantially outperforms vanilla GRPO. Our code and models are available at https://github.com/T-Lab-CUHKSZ/G2RPO-A.

Fine-tuning pre-trained generative models with Reinforcement Learning (RL) has emerged as an effective approach for aligning outputs more closely with nuanced human preferences. In this paper, we investigate the application of Group Relative Policy Optimization (GRPO) to fine-tune next-scale visual autoregressive (VAR) models. Our empirical results demonstrate that this approach enables alignment to intricate reward signals derived from aesthetic predictors and CLIP embeddings, significantly enhancing image quality and enabling precise control over the generation style. Interestingly, by leveraging CLIP, our method can help VAR models generalize beyond their initial ImageNet distribution: through RL-driven exploration, these models can generate images aligned with prompts referencing image styles that were absent during pre-training. In summary, we show that RL-based fine-tuning is both efficient and effective for VAR models, benefiting particularly from their fast inference speeds, which are advantageous for online sampling, an aspect that poses significant challenges for diffusion-based alternatives.

To keep pace with the increasing pace of large language models (LLM) development, model output evaluation has transitioned away from time-consuming human evaluation to automatic evaluation, where LLMs themselves are tasked with assessing and critiquing other model outputs. LLM-as-judge models are a class of generative evaluators that excel in evaluating relatively simple domains, like chat quality, but struggle in reasoning intensive domains where model responses contain more substantive and challenging content. To remedy existing judge shortcomings, we explore training judges with reinforcement learning (RL). We make three key contributions: (1) We propose the Equivalent Initial State Group Relative Policy Optimization (EIS-GRPO) algorithm, which allows us to train our judge to be robust to positional biases that arise in more complex evaluation settings. (2) We introduce ReasoningJudgeBench, a benchmark that evaluates judges in diverse reasoning settings not covered by prior work. (3) We train Judge for Reasoning (J4R), a 7B judge trained with EIS-GRPO that outperforms GPT-4o and the next best small judge by 6.7% and 9%, matching or exceeding the performance of larger GRPO-trained judges on both JudgeBench and ReasoningJudgeBench.

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

Off-policy reinforcement learning (RL) for large language models (LLMs) is attracting growing interest, driven by practical constraints in real-world applications, the complexity of LLM-RL infrastructure, and the need for further innovations of RL methodologies. While classic REINFORCE and its modern variants like Group Relative Policy Optimization (GRPO) are typically regarded as on-policy algorithms with limited tolerance of off-policyness, we present in this work a first-principles derivation for group-relative REINFORCE without assuming a specific training data distribution, showing that it admits a native off-policy interpretation. This perspective yields two general principles for adapting REINFORCE to off-policy settings: regularizing policy updates, and actively shaping the data distribution. Our analysis demystifies some myths about the roles of importance sampling and clipping in GRPO, unifies and reinterprets two recent algorithms -- Online Policy Mirror Descent (OPMD) and Asymmetric REINFORCE (AsymRE) -- as regularized forms of the REINFORCE loss, and offers theoretical justification for seemingly heuristic data-weighting strategies. Our findings lead to actionable insights that are validated with extensive empirical studies, and open up new opportunities for principled algorithm design in off-policy RL for LLMs. Source code for this work is available at https://github.com/modelscope/Trinity-RFT/tree/main/examples/rec_gsm8k.

We propose Fuzzy Group Relative Policy Reward (FGRPR), a novel framework that integrates Group Relative Policy Optimization (GRPO) with a fuzzy reward function to enhance learning efficiency. Unlike the conventional binary 0/1 accuracy reward, our fuzzy reward model provides nuanced incentives, encouraging more precise outputs. Experimental results demonstrate that GRPO with a standard 0/1 accuracy reward underperforms compared to supervised fine-tuning (SFT). In contrast, FGRPR, applied to Qwen2.5-VL(3B and 7B), surpasses all baseline models, including GPT4o, LLaMA2(90B), and SFT, across five in-domain datasets. On an out-of-domain dataset, FGRPR achieves performance comparable to SFT but excels when target values are larger, as its fuzzy reward function assigns higher rewards to closer approximations. This approach is broadly applicable to tasks where the precision of the answer is critical. Code and data: https://github.com/yeyimilk/CrowdVLM-R1

Policy-based optimizations are widely adopted today for the training and alignment of language models, where one of the most recent and effective approaches is Group-relative Policy Optimization (GRPO). In this paper, we reveals and analyze two major limitations of GRPO: (i) tokens frequently appear in completions with both positive and negative rewards, leading to conflicting gradient updates that can reduce their output probability, even though can be essential for maintaining proper structure; (ii) negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, progressively flattening the output distribution and degrading learning. To address these issues and provide a more stable and effective policy optimization strategy, we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which identifies conflict tokens, tokens appearing in the same position across completions with opposite rewards, protects them by skipping negative updates, while amplifying positive ones. To further prevent policy collapse, GTPO filters out completions whose entropy exceeds a provable threshold. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, validated through multiple experiments on GSM8K, MATH and AIME 2024 benchmarks.

Reinforcement fine-tuning (RFT) is essential for enhancing the reasoning capabilities of large language models (LLM), yet the widely adopted Group Relative Policy Optimization (GRPO) suffers from entropy collapse, where entropy monotonically decreases, exploration vanishes, and policies converge prematurely. Existing entropy-regularized methods only partially alleviate this issue while introducing bias and instability, leaving entropy control unresolved and the connection between entropy, exploration, and performance unclear. We propose Arbitrary Entropy Policy Optimization (AEPO), which eliminates entropy collapse by replacing entropy bonuses with REINFORCE policy gradient on temperature-adjusted distributions and stabilizing entropy through temperature regulation. AEPO integrates three key designs: policy gradient as regularization, distribution as regularization, and REINFORCE as regularization, enabling precise entropy control without distorting optimization. Experiments demonstrate three major contributions: AEPO (1) stabilizes entropy at arbitrary target levels, effectively removing collapse in GRPO; (2) reveals a non-monotonic relation where performance first improves then declines with increasing entropy, clarifying the link between entropy, exploration, and reasoning; and (3) generalizes beyond entropy, providing a broader RFT paradigm where superior target distributions can serve as REINFORCE regularizers.

RAG systems are increasingly deployed in high-stakes domains where users expect outputs to be consistent across semantically equivalent queries. However, existing systems often exhibit significant inconsistencies due to variability in both the retriever and generator (LLM), undermining trust and reliability. In this work, we focus on information consistency, i.e., the requirement that outputs convey the same core content across semantically equivalent inputs. We introduce a principled evaluation framework that decomposes RAG consistency into retriever-level, generator-level, and end-to-end components, helping identify inconsistency sources. To improve consistency, we propose Paraphrased Set Group Relative Policy Optimization (PS-GRPO), an RL approach that leverages multiple rollouts across paraphrased set to assign group similarity rewards. We leverage PS-GRPO to achieve Information Consistent RAG (Con-RAG), training the generator to produce consistent outputs across paraphrased queries and remain robust to retrieval-induced variability. Because exact reward computation over paraphrase sets is computationally expensive, we also introduce a scalable approximation method that retains effectiveness while enabling efficient, large-scale training. Empirical evaluations across short-form, multi-hop, and long-form QA benchmarks demonstrate that Con-RAG significantly improves both consistency and accuracy over strong baselines, even in the absence of explicit ground-truth supervision. Our work provides practical solutions for evaluating and building reliable RAG systems for safety-critical deployments.

Applying Reinforcement Learning (RL) to Video Large Language Models (Video-LLMs) shows significant promise for complex video reasoning. However, popular Reinforcement Fine-Tuning (RFT) methods, such as outcome-based Group Relative Policy Optimization (GRPO), are limited by data preparation bottlenecks (e.g., noise or high cost) and exhibit unstable improvements in the quality of long chain-of-thoughts (CoTs) and downstream performance.To address these limitations, we propose VerIPO, a Verifier-guided Iterative Policy Optimization method designed to gradually improve video LLMs' capacity for generating deep, long-term reasoning chains. The core component is Rollout-Aware Verifier, positioned between the GRPO and Direct Preference Optimization (DPO) training phases to form the GRPO-Verifier-DPO training loop. This verifier leverages small LLMs as a judge to assess the reasoning logic of rollouts, enabling the construction of high-quality contrastive data, including reflective and contextually consistent CoTs. These curated preference samples drive the efficient DPO stage (7x faster than GRPO), leading to marked improvements in reasoning chain quality, especially in terms of length and contextual consistency. This training loop benefits from GRPO's expansive search and DPO's targeted optimization. Experimental results demonstrate: 1) Significantly faster and more effective optimization compared to standard GRPO variants, yielding superior performance; 2) Our trained models exceed the direct inference of large-scale instruction-tuned Video-LLMs, producing long and contextually consistent CoTs on diverse video reasoning tasks; and 3) Our model with one iteration outperforms powerful LMMs (e.g., Kimi-VL) and long reasoning models (e.g., Video-R1), highlighting its effectiveness and stability.

Reinforcement learning (RL) has become central to enhancing reasoning in large language models (LLMs). Yet on-policy algorithms such as Group Relative Policy Optimization (GRPO) often suffer in early training: noisy gradients from low-quality rollouts lead to unstable updates and inefficient exploration. We introduce Slow-Fast Policy Optimization (SFPO), a simple yet efficient framework to address these limitations via decomposing each step into three stages: a short fast trajectory of inner steps on the same batch, a reposition mechanism to control off-policy drift, and a final slow correction. This reposition-before-update design preserves the objective and rollout process unchanged, making SFPO plug-compatible with existing policy-gradient pipelines. Extensive experiments demonstrate that SFPO consistently improves stability, reduces rollouts, and accelerates convergence of reasoning RL training. Specifically, it outperforms GRPO by up to 2.80 points in average on math reasoning benchmarks. It also achieves up to 4.93 fewer rollouts and a 4.19 reduction in wall-clock time to match GRPO's best accuracy.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

Large language models (LLMs) exhibit varying levels of confidence across input prompts (questions): some lead to consistent, semantically similar answers, while others yield diverse or contradictory outputs. This variation reflects LLM's uncertainty about the input prompt, a signal of how confidently the model understands a given problem. However, vanilla Group Relative Policy Optimization (GRPO) treats all prompts equally during policy updates, ignoring this important information about the model's knowledge boundaries. To address this limitation, we propose SEED-GRPO (Semantic Entropy EnhanceD GRPO), which explicitly measures LLMs' uncertainty of the input prompts semantic entropy. Semantic entropy measures the diversity of meaning in multiple generated answers given a prompt and uses this to modulate the magnitude of policy updates. This uncertainty-aware training mechanism enables dynamic adjustment of policy update magnitudes based on question uncertainty. It allows more conservative updates on high-uncertainty questions while maintaining the original learning signal on confident ones. Experimental results on five mathematical reasoning benchmarks (AIME24 56.7, AMC 68.7, MATH 83.4, Minerva 34.2, and OlympiadBench 48.0) demonstrate that SEED-GRPO achieves new state-of-the-art performance in average accuracy, validating the effectiveness of uncertainty-aware policy optimization.

Recent advancements, such as Group Relative Policy Optimization (GRPO), have enhanced the reasoning capabilities of large language models by optimizing the arithmetic mean of token-level rewards. However, GRPO suffers from unstable policy updates when processing tokens with outlier importance-weighted rewards, which manifests as extreme importance sampling ratios during training, i.e., the ratio between the sampling probabilities assigned to a token by the current and old policies. In this work, we propose Geometric-Mean Policy Optimization (GMPO), a stabilized variant of GRPO. Instead of optimizing the arithmetic mean, GMPO maximizes the geometric mean of token-level rewards, which is inherently less sensitive to outliers and maintains a more stable range of importance sampling ratio. In addition, we provide comprehensive theoretical and experimental analysis to justify the design and stability benefits of GMPO. Beyond improved stability, GMPO-7B outperforms GRPO by an average of 4.1% on multiple mathematical benchmarks and 1.4% on multimodal reasoning benchmark, including AIME24, AMC, MATH500, OlympiadBench, Minerva, and Geometry3K. Code is available at https://github.com/callsys/GMPO.

Emerging embodied AI applications, such as wearable cameras and autonomous agents, have underscored the need for robust reasoning from first person video streams. We introduce EgoVLM, a vision-language model specifically designed to integrate visual comprehension and spatial-temporal reasoning within egocentric video contexts. EgoVLM is fine-tuned via Group Relative Policy Optimization (GRPO), a reinforcement learning method adapted to align model outputs with human-like reasoning steps. Following DeepSeek R1-Zero's approach, we directly tune using RL without any supervised fine-tuning phase on chain-of-thought (CoT) data. We evaluate EgoVLM on egocentric video question answering benchmarks and show that domain-specific training substantially improves performance over general-purpose VLMs. Our EgoVLM-3B, trained exclusively on non-CoT egocentric data, outperforms the base Qwen2.5-VL 3B and 7B models by 14.33 and 13.87 accuracy points on the EgoSchema benchmark, respectively. By explicitly generating reasoning traces, EgoVLM enhances interpretability, making it well-suited for downstream applications. Furthermore, we introduce a novel keyframe-based reward that incorporates salient frame selection to guide reinforcement learning optimization. This reward formulation opens a promising avenue for future exploration in temporally grounded egocentric reasoning.

In this paper, we introduce a Group Relative Policy Optimization (GRPO)-based method for training Speech-Aware Large Language Models (SALLMs) on open-format speech understanding tasks, such as Spoken Question Answering and Automatic Speech Translation. SALLMs have proven highly effective for speech understanding tasks. GRPO has recently gained traction for its efficiency in training LLMs, and prior work has explored its application to SALLMs, primarily in multiple-choice tasks. Building on this, we focus on open-format tasks that better reflect the generative abilities of the models. Our approach leverages GRPO with BLEU as the reward signal to optimize SALLMs, and we demonstrate empirically that it surpasses standard SFT across several key metrics. Finally, we explore the potential of incorporating off-policy samples within GRPO for these tasks, highlighting avenues for further improvement and further research.

Large language models (LLMs) excel at general mathematical reasoning but fail catastrophically on specialized technical mathematics. In wireless communications, where problems require precise manipulation of information-theoretic bounds, optimization constraints, and signal processing formulations, even state-of-the-art models struggle to achieve competent performance. We present WirelessMathLM, demonstrating that compact models (0.5B-7B parameters) can match or exceed much larger models through domain-specific reinforcement learning with verifiable rewards. Our key insight is that wireless mathematics problems possess a unique property--verifiable correctness--that enables effective reinforcement learning without human feedback. We construct WirelessMathBench-XL, a comprehensive benchmark of 4,027 problems from 970 papers. Using Group Relative Policy Optimization (GRPO) with binary verification rewards, we train models directly from base checkpoints without supervised warm-start. Our 7B model achieves 39.5% accuracy on WirelessMathBench-XL, approaching GPT-4o (40.4%) while using about 100 times fewer parameters than DeepSeek-R1 (671B, 57.4%). Remarkably, GRPO training nearly doubles performance across all model scales (0.5B +11%, 3B +103%, 7B +81%), with positive transfer to general mathematics benchmarks--our models gain +8.4 points on average across MATH, Minerva-Math, OlympiadBench, AMC, and AIME without any training on these tasks.

Enhancing the reasoning capabilities of large language models (LLMs) typically relies on massive computational resources and extensive datasets, limiting accessibility for resource-constrained settings. Our study investigates the potential of reinforcement learning (RL) to improve reasoning in small LLMs, focusing on a 1.5-billion-parameter model, DeepSeek-R1-Distill-Qwen-1.5B, under strict constraints: training on 4 NVIDIA A40 GPUs (48 GB VRAM each) within 24 hours. Adapting the Group Relative Policy Optimization (GRPO) algorithm and curating a compact, high-quality mathematical reasoning dataset, we conducted three experiments to explore model behavior and performance. Our results demonstrate rapid reasoning gains - e.g., AMC23 accuracy rising from 63% to 80% and AIME24 reaching 46.7%, surpassing o1-preview - using only 7,000 samples and a $42 training cost, compared to thousands of dollars for baseline models. However, challenges such as optimization instability and length constraints emerged with prolonged training. These findings highlight the efficacy of RL-based fine-tuning for small LLMs, offering a cost-effective alternative to large-scale approaches. We release our code and datasets as open-source resources, providing insights into trade-offs and laying a foundation for scalable, reasoning-capable LLMs in resource-limited environments. All are available at https://github.com/knoveleng/open-rs.

Group-Relative Policy Optimization (GRPO) is a key technique for training large reasoning models, yet it suffers from a critical vulnerability: the Think-Answer Mismatch, where noisy reward signals corrupt the learning process. This problem is most severe in unbalanced response groups, paradoxically degrading the signal precisely when it should be most informative. To address this challenge, we propose Stable Group-Relative Policy Optimization (S-GRPO), a principled enhancement that derives optimal, noise-aware advantage weights to stabilize training. Our comprehensive experiments on mathematical reasoning benchmarks demonstrate S-GRPO's effectiveness and robustness. On various models, S-GRPO significantly outperforms DR. GRPO, achieving performance gains of +2.5% on Qwen-Math-7B-Base, +2.2% on Llama-3.2-3B-Base, and +2.4% on Qwen-Math-1.5B-Instruct. Most critically, while standard GRPO fails to learn under 20% synthetic reward noise, S-GRPO maintains stable learning progress. These results highlight S-GRPO's potential for more robust and effective training of large-scale reasoning models. \footnote{Code and data are available at: https://github.com/shenpeijun0212/S-GRPO

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to mismatches between the training data's difficulty and the model's capability. LLMs fail to discover viable reasoning paths when problems are overly difficult, while learning little new capability when problems are too simple. In this work, we formalize the impact of problem difficulty by quantifying the relationship between loss descent speed and rollout accuracy. Building on this analysis, we propose SEELE, a novel supervision-aided RLVR framework that dynamically adjusts problem difficulty to stay within the high-efficiency region. SEELE augments each training sample by appending a hint (part of a full solution) after the original problem. Unlike previous hint-based approaches, SEELE deliberately and adaptively adjusts the hint length for each problem to achieve an optimal difficulty. To determine the optimal hint length, SEELE employs a multi-round rollout sampling strategy. In each round, it fits an item response theory model to the accuracy-hint pairs collected in preceding rounds to predict the required hint length for the next round. This instance-level, real-time difficulty adjustment aligns problem difficulty with the evolving model capability, thereby improving exploration efficiency. Experimental results show that SEELE outperforms Group Relative Policy Optimization (GRPO) and Supervised Fine-tuning (SFT) by +11.8 and +10.5 points, respectively, and surpasses the best previous supervision-aided approach by +3.6 points on average across six math reasoning benchmarks.

This study investigates the spatial reasoning capabilities of vision-language models (VLMs) through Chain-of-Thought (CoT) prompting and reinforcement learning. We begin by evaluating the impact of different prompting strategies and find that simple CoT formats, where the model generates a reasoning step before the answer, not only fail to help, but can even harm the model's original performance. In contrast, structured multi-stage prompting based on scene graphs (SceneGraph CoT) significantly improves spatial reasoning accuracy. Furthermore, to improve spatial reasoning ability, we fine-tune models using Group Relative Policy Optimization (GRPO) on the SAT dataset and evaluate their performance on CVBench. Compared to supervised fine-tuning (SFT), GRPO achieves higher accuracy on Pass@1 evaluations and demonstrates superior robustness under out-of-distribution (OOD) conditions. In particular, we find that SFT overfits to surface-level linguistic patterns and may degrade performance when test-time phrasing changes (e.g., from "closer to" to "farther from"). GRPO, on the other hand, generalizes more reliably and maintains stable performance under such shifts. Our findings provide insights into how reinforcement learning and structured prompting improve the spatial reasoning capabilities and generalization behavior of modern VLMs. All code is open source at: https://github.com/Yvonne511/spatial-vlm-investigator

Recent works on large language models (LLMs) have successfully demonstrated the emergence of reasoning capabilities via reinforcement learning (RL). Although recent efforts leverage group relative policy optimization (GRPO) for MLLMs post-training, they constantly explore one specific aspect, such as grounding tasks, math problems, or chart analysis. There are no works that can leverage multi-source MLLM tasks for stable reinforcement learning. In this work, we present a unified perspective to solve this problem. We present Mixed-R1, a unified yet straightforward framework that contains a mixed reward function design (Mixed-Reward) and a mixed post-training dataset (Mixed-45K). We first design a data engine to select high-quality examples to build the Mixed-45K post-training dataset. Then, we present a Mixed-Reward design, which contains various reward functions for various MLLM tasks. In particular, it has four different reward functions: matching reward for binary answer or multiple-choice problems, chart reward for chart-aware datasets, IoU reward for grounding problems, and open-ended reward for long-form text responses such as caption datasets. To handle the various long-form text content, we propose a new open-ended reward named Bidirectional Max-Average Similarity (BMAS) by leveraging tokenizer embedding matching between the generated response and the ground truth. Extensive experiments show the effectiveness of our proposed method on various MLLMs, including Qwen2.5-VL and Intern-VL on various sizes. Our dataset and model are available at https://github.com/xushilin1/mixed-r1.

We introduce Entropy-Guided Sequence Weighting (EGSW), a novel approach that enhances the exploration-exploitation tradeoff by dynamically assigning weights to generated outputs based on their advantage and entropy for Reinforcement Learning-based Large Language Model fine-tuning. EGSW integrates entropy regularization with advantage-based weighting to balance policy updates, enabling efficient exploration in high-dimensional state spaces. By employing temperature-scaled softmax weighting over sequences, EGSW prioritizing high-reward, high-uncertainty steps while maintaining training stability. Although originally developed to improve Group Relative Policy Optimization (GRPO) during large language model (LLM) fine-tuning, EGSW is generalizable to other reinforcement learning (RL) algorithms and can be implemented in both step-wise and trajectory-wise settings. Empirical evaluations demonstrate that EGSW enhances GRPO reasoning ability, yielding improvements in sample efficiency. Future work will explore the application of EGSW to advanced RL methodologies.

Recent advances in R1-like reasoning models leveraging Group Relative Policy Optimization (GRPO) have significantly improved the performance of language models on mathematical reasoning tasks. However, current GRPO implementations encounter critical challenges, including reward sparsity due to binary accuracy metrics, limited incentives for conciseness, and insufficient focus on complex reasoning tasks. To address these issues, we propose GRPO-LEAD, a suite of novel enhancements tailored for mathematical reasoning. Specifically, GRPO-LEAD introduces (1) a length-dependent accuracy reward to encourage concise and precise solutions, (2) an explicit penalty mechanism for incorrect answers to sharpen decision boundaries, and (3) a difficulty-aware advantage reweighting strategy that amplifies learning signals for challenging problems. Furthermore, we systematically examine the impact of model scale and supervised fine-tuning (SFT) strategies, demonstrating that larger-scale base models and carefully curated datasets significantly enhance reinforcement learning effectiveness. Extensive empirical evaluations and ablation studies confirm that GRPO-LEAD substantially mitigates previous shortcomings, resulting in language models that produce more concise, accurate, and robust reasoning across diverse mathematical tasks.

The remarkable capabilities of modern large reasoning models are largely unlocked through post-training techniques such as supervised fine-tuning and reinforcement learning. However, the architectural mechanisms behind such improvements remain largely opaque. In this work, we use circuit analysis to demonstrate that post-training for complex reasoning sparks the emergence of novel, functionally specialized attention heads. These heads collectively support structured reasoning and computation. Our comparative analysis across Qwen families and DeepSeek-distilled model reveals that these emergent heads evolve differently under different training regimes. Distillation and SFT foster a cumulative addition of stable reasoning heads. In contrast, group relative policy optimization operates in a dynamic search mode: relatively few attention heads are iteratively activated, evaluated, and pruned, with their survival closely tracking fluctuations in the task reward signal. Furthermore, we find that controllable think on/off models do not possess dedicated thinking heads. Instead, turning off explicit reasoning triggers a broader-but less efficient-set of compensatory heads. Through ablation and qualitative analyses, we connect these circuit-level dynamics to a crucial performance trade-off: strengthened heads enable sophisticated problem-solving strategies for difficult problems but can also introduce over-thinking failure modes, such as calculation errors or logical loops on simpler tasks. These findings connect circuit-level dynamics to macro-level performance, identifying an inherent tension where complex reasoning comes at the cost of elementary computations. More broadly, our work points to future directions for training policy design, emphasizing the need to balance the development of effective reasoning strategies with the assurance of reliable, flawless execution.

Recent progress in aligning image and video generative models with Group Relative Policy Optimization (GRPO) has improved human preference alignment, but existing variants remain inefficient due to sequential rollouts and large numbers of sampling steps, unreliable credit assignment: sparse terminal rewards are uniformly propagated across timesteps, failing to capture the varying criticality of decisions during denoising. In this paper, we present BranchGRPO, a method that restructures the rollout process into a branching tree, where shared prefixes amortize computation and pruning removes low-value paths and redundant depths. BranchGRPO introduces three contributions: (1) a branching scheme that amortizes rollout cost through shared prefixes while preserving exploration diversity; (2) a reward fusion and depth-wise advantage estimator that transforms sparse terminal rewards into dense step-level signals; and (3) pruning strategies that cut gradient computation but leave forward rollouts and exploration unaffected. On HPDv2.1 image alignment, BranchGRPO improves alignment scores by up to 16\% over DanceGRPO, while reducing per-iteration training time by nearly 55\%. A hybrid variant, BranchGRPO-Mix, further accelerates training to 4.7x faster than DanceGRPO without degrading alignment. On WanX video generation, it further achieves higher Video-Align scores with sharper and temporally consistent frames compared to DanceGRPO. Codes are available at https://fredreic1849.github.io/BranchGRPO-Webpage/{BranchGRPO}.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

Large language models (LLMs) have demonstrated strong capabilities in translating natural language questions about relational databases into SQL queries. In particular, test-time scaling techniques such as Self-Consistency and Self-Correction can enhance SQL generation accuracy by increasing computational effort during inference. However, these methods have notable limitations: Self-Consistency may select suboptimal outputs despite majority votes, while Self-Correction typically addresses only syntactic errors. To leverage the strengths of both approaches, we propose CSC-SQL, a novel method that integrates Self-Consistency and Self-Correction. CSC-SQL selects the two most frequently occurring outputs from parallel sampling and feeds them into a merge revision model for correction. Additionally, we employ the Group Relative Policy Optimization (GRPO) algorithm to fine-tune both the SQL generation and revision models via reinforcement learning, significantly enhancing output quality. Experimental results confirm the effectiveness and generalizability of CSC-SQL. On the BIRD development set, our 3B model achieves 65.28% execution accuracy, while the 7B model achieves 69.19%. The code will be open sourced at https://github.com/CycloneBoy/csc_sql.

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

Training robust and generalizable reward models for human visual preferences is essential for aligning text-to-image and text-to-video generative models with human intent. However, current reward models often fail to generalize, and supervised fine-tuning leads to memorization, demanding complex annotation pipelines. While reinforcement learning (RL), specifically Group Relative Policy Optimization (GRPO), improves generalization, we uncover a key failure mode: a significant drop in reasoning accuracy occurs when a model's reasoning trace contradicts that of an independent, frozen vision-language model ("listener") evaluating the same output. To address this, we introduce a listener-augmented GRPO framework. Here, the listener re-evaluates the reasoner's chain-of-thought to provide a dense, calibrated confidence score, shaping the RL reward signal. This encourages the reasoner not only to answer correctly, but to produce explanations that are persuasive to an independent model. Our listener-shaped reward scheme achieves best accuracy on the ImageReward benchmark (67.4%), significantly improves out-of-distribution (OOD) performance on a large-scale human preference dataset (1.2M votes, up to +6% over naive reasoner), and reduces reasoning contradictions compared to strong GRPO and SFT baselines. These results demonstrate that listener-based rewards provide a scalable, data-efficient path to aligning vision-language models with nuanced human preferences. We will release our reasoning model here: https://huggingface.co/alexgambashidze/qwen2.5vl_image_preference_reasoner.

Multimodal large language models (MLLMs) have advanced perception across text, vision, and audio, yet they often struggle with structured cross-modal reasoning, particularly when integrating audio and visual signals. We introduce EchoInk-R1, a reinforcement learning framework that enhances such reasoning in MLLMs. Built upon the Qwen2.5-Omni-7B foundation and optimized with Group Relative Policy Optimization (GRPO), EchoInk-R1 tackles multiple-choice question answering over synchronized audio-image pairs. To enable this, we curate AVQA-R1-6K, a dataset pairing such audio-image inputs with multiple-choice questions derived from OmniInstruct-v1. EchoInk-R1-7B achieves 85.77% accuracy on the validation set, outperforming the base model, which scores 80.53%, using only 562 reinforcement learning steps. Beyond accuracy, EchoInk-R1 demonstrates reflective reasoning by revisiting initial interpretations and refining responses when facing ambiguous multimodal inputs. These results suggest that lightweight reinforcement learning fine-tuning enhances cross-modal reasoning in MLLMs. EchoInk-R1 is the first framework to unify audio, visual, and textual modalities for general open-world reasoning via reinforcement learning. Code and data are publicly released to facilitate further research.

Training vision-language models (VLMs) for complex reasoning remains a challenging task, i.a. due to the scarcity of high-quality image-text reasoning data. Conversely, text-based reasoning resources are abundant and scalable, but it is still an open question how to leveraging them for VLM reasoning. To address this problem, we propose VOLD, a framework to transfer reasoning capabilities from text-only teacher models to VLM student models. To this end, VOLD combines reinforcement learning via Group Relative Policy Optimization (GRPO) with on-policy distillation, which allows the student reasoning traces to be guided by the teacher model, resulting in a significant gain over using GRPO alone. We further show that a cold-start alignment is essential for an effective transfer during the online training phase in this scenario and that without sufficient distributional alignment between teacher and student, on-policy distillation fails to provide meaningful guidance. We evaluate VOLD across diverse benchmarks including MMMU-Pro, MathVision, MathVista, and LogicVista, showing that VOLD outperforms the baseline model significantly and improves over the state of the art by a margin. Our ablation shows the importance of a cold-start alignment via SFT for on-policy distillation with a text-only teacher.

Recent advances at the intersection of reinforcement learning (RL) and visual intelligence have enabled agents that not only perceive complex visual scenes but also reason, generate, and act within them. This survey offers a critical and up-to-date synthesis of the field. We first formalize visual RL problems and trace the evolution of policy-optimization strategies from RLHF to verifiable reward paradigms, and from Proximal Policy Optimization to Group Relative Policy Optimization. We then organize more than 200 representative works into four thematic pillars: multi-modal large language models, visual generation, unified model frameworks, and vision-language-action models. For each pillar we examine algorithmic design, reward engineering, benchmark progress, and we distill trends such as curriculum-driven training, preference-aligned diffusion, and unified reward modeling. Finally, we review evaluation protocols spanning set-level fidelity, sample-level preference, and state-level stability, and we identify open challenges that include sample efficiency, generalization, and safe deployment. Our goal is to provide researchers and practitioners with a coherent map of the rapidly expanding landscape of visual RL and to highlight promising directions for future inquiry. Resources are available at: https://github.com/weijiawu/Awesome-Visual-Reinforcement-Learning.

Vision-language models (VLMs) have advanced reasoning in natural scenes, but their role in medical imaging remains underexplored. Medical reasoning tasks demand robust image analysis and well-justified answers, posing challenges due to the complexity of medical images. Transparency and trustworthiness are essential for clinical adoption and regulatory compliance. We introduce Med-R1, a framework exploring reinforcement learning (RL) to enhance VLMs' generalizability and trustworthiness in medical reasoning. Leveraging the DeepSeek strategy, we employ Group Relative Policy Optimization (GRPO) to guide reasoning paths via reward signals. Unlike supervised fine-tuning (SFT), which often overfits and lacks generalization, RL fosters robust and diverse reasoning. Med-R1 is evaluated across eight medical imaging modalities: CT, MRI, Ultrasound, Dermoscopy, Fundus Photography, Optical Coherence Tomography (OCT), Microscopy, and X-ray Imaging. Compared to its base model, Qwen2-VL-2B, Med-R1 achieves a 29.94% accuracy improvement and outperforms Qwen2-VL-72B, which has 36 times more parameters. Testing across five question types-modality recognition, anatomy identification, disease diagnosis, lesion grading, and biological attribute analysis Med-R1 demonstrates superior generalization, exceeding Qwen2-VL-2B by 32.06% and surpassing Qwen2-VL-72B in question-type generalization. These findings show that RL improves medical reasoning and enables parameter-efficient models to outperform significantly larger ones. With interpretable reasoning outputs, Med-R1 represents a promising step toward generalizable, trustworthy, and clinically viable medical VLMs.

Recent advancements in the reasoning capabilities of large language models (LLMs) show that employing group relative policy optimization (GRPO) algorithm for reinforcement learning (RL) training allows the models to use more thinking/reasoning tokens for generating better responses. However, LLMs can generate only a finite amount of tokens while maintaining attention to the previously generated tokens. This limit, also known as the context size of an LLM, is a bottleneck in LLM reasoning with arbitrarily large number of tokens. To think beyond the limit of context size, an LLM must employ a modular thinking strategy to reason over multiple rounds. In this work, we propose MOTIF: Modular Thinking via Reinforcement Finetuning -- an RL training method for generating thinking tokens in multiple rounds, effectively allowing the model to think with additional context size. We trained the open-source model Qwen2.5-3B-Instruct on GSM8K dataset via parameter efficient fine-tuning and tested its accuracy on MATH500 and AIME2024 benchmarks. Our experiments show 3.8\% and 3.3\% improvements over vanilla GRPO based training in the respective benchmarks. Furthermore, this improvement was achieved with only 15\% of samples, thus demonstrating sample efficiency of MOTIF. Our code and models are available at https://github.com/purbeshmitra/MOTIF and https://huggingface.co/purbeshmitra/MOTIF, respectively.

Reasoning has emerged as a pivotal capability in Large Language Models (LLMs). Through Reinforcement Learning (RL), typically Group Relative Policy Optimization (GRPO), these models are able to solve complex tasks such as mathematics and code generation. Building on these advances, recent research has sought to extend reasoning to Vision-Language Models (VLMs), yielding promising results across diverse visual tasks. Despite this progress, our study uncovers the dual nature of multimodal reasoning: while it substantially enhances logical inference and facilitates performance on challenging problems, it may gradually impair perceptual grounding, leading to recognition failures on otherwise basic visual questions. Through further analysis, we attribute this phenomenon to visual forgetting, wherein prolonged reasoning causes the model to increasingly disregard visual input. To address this, we propose Vision-Anchored Policy Optimization (VAPO), a simple yet effective method that explicitly steers the reasoning process toward visually grounded trajectories. Our result model, VAPO-Thinker-7B, significantly strengthens the model's reliance on visual information and achieves new state-of-the-art results on a wide range of established benchmarks. Project page: https://xytian1008.github.io/VAPO/

DeepSeek-R1-Zero has successfully demonstrated the emergence of reasoning capabilities in LLMs purely through Reinforcement Learning (RL). Inspired by this breakthrough, we explore how RL can be utilized to enhance the reasoning capability of MLLMs. However, direct training with RL struggles to activate complex reasoning capabilities such as questioning and reflection in MLLMs, due to the absence of substantial high-quality multimodal reasoning data. To address this issue, we propose the reasoning MLLM, Vision-R1, to improve multimodal reasoning capability. Specifically, we first construct a high-quality multimodal CoT dataset without human annotations by leveraging an existing MLLM and DeepSeek-R1 through modality bridging and data filtering to obtain a 200K multimodal CoT dataset, Vision-R1-cold dataset. It serves as cold-start initialization data for Vision-R1. To mitigate the optimization challenges caused by overthinking after cold start, we propose Progressive Thinking Suppression Training (PTST) strategy and employ Group Relative Policy Optimization (GRPO) with the hard formatting result reward function to gradually refine the model's ability to learn correct and complex reasoning processes on a 10K multimodal math dataset. Comprehensive experiments show our model achieves an average improvement of sim6% across various multimodal math reasoning benchmarks. Vision-R1-7B achieves a 73.5% accuracy on the widely used MathVista benchmark, which is only 0.4% lower than the leading reasoning model, OpenAI O1. The datasets and code will be released in: https://github.com/Osilly/Vision-R1 .

Effective reasoning remains a core challenge for large language models (LLMs) in the financial domain, where tasks often require domain-specific knowledge, precise numerical calculations, and strict adherence to compliance rules. We propose DianJin-R1, a reasoning-enhanced framework designed to address these challenges through reasoning-augmented supervision and reinforcement learning. Central to our approach is DianJin-R1-Data, a high-quality dataset constructed from CFLUE, FinQA, and a proprietary compliance corpus (Chinese Compliance Check, CCC), combining diverse financial reasoning scenarios with verified annotations. Our models, DianJin-R1-7B and DianJin-R1-32B, are fine-tuned from Qwen2.5-7B-Instruct and Qwen2.5-32B-Instruct using a structured format that generates both reasoning steps and final answers. To further refine reasoning quality, we apply Group Relative Policy Optimization (GRPO), a reinforcement learning method that incorporates dual reward signals: one encouraging structured outputs and another rewarding answer correctness. We evaluate our models on five benchmarks: three financial datasets (CFLUE, FinQA, and CCC) and two general reasoning benchmarks (MATH-500 and GPQA-Diamond). Experimental results show that DianJin-R1 models consistently outperform their non-reasoning counterparts, especially on complex financial tasks. Moreover, on the real-world CCC dataset, our single-call reasoning models match or even surpass the performance of multi-agent systems that require significantly more computational cost. These findings demonstrate the effectiveness of DianJin-R1 in enhancing financial reasoning through structured supervision and reward-aligned learning, offering a scalable and practical solution for real-world applications.

Visual retrieval-augmented generation (VRAG) augments vision-language models (VLMs) with external visual knowledge to ground reasoning and reduce hallucinations. Yet current VRAG systems often fail to reliably perceive and integrate evidence across multiple images, leading to weak grounding and erroneous conclusions. In this paper, we propose EVisRAG, an end-to-end framework that learns to reason with evidence-guided multi-image to address this issue. The model first observes retrieved images and records per-image evidence, then derives the final answer from the aggregated evidence. To train EVisRAG effectively, we introduce Reward-Scoped Group Relative Policy Optimization (RS-GRPO), which binds fine-grained rewards to scope-specific tokens to jointly optimize visual perception and reasoning abilities of VLMs. Experimental results on multiple visual question answering benchmarks demonstrate that EVisRAG delivers substantial end-to-end gains over backbone VLM with 27\% improvements on average. Further analysis shows that, powered by RS-GRPO, EVisRAG improves answer accuracy by precisely perceiving and localizing question-relevant evidence across multiple images and deriving the final answer from that evidence, much like a real detective.

We present a two-stage fine-tuning approach to make the large language model Qwen3 14B "think" natively in Korean. In the first stage, supervised fine-tuning (SFT) on a high-quality Korean reasoning dataset establishes a strong foundation in Korean logical reasoning, yielding notable improvements in Korean-language tasks and even some gains in general reasoning ability. In the second stage, we employ reinforcement learning with a customized Group Relative Policy Optimization (GRPO) algorithm to further enhance both Korean reasoning alignment and overall problem-solving performance. We address critical stability challenges in GRPO training - such as reward hacking and policy collapse - by introducing an oracle judge model that calibrates the reward signal. Our approach achieves stable learning (avoiding the collapse observed in naive GRPO) and leads to steady, incremental performance gains. The final RL-tuned model demonstrates substantially improved results on advanced reasoning benchmarks (particularly math and coding tasks) while maintaining knowledge and language proficiency, successfully conducting its internal chain-of-thought entirely in Korean.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

Cinematography, the fundamental visual language of film, is essential for conveying narrative, emotion, and aesthetic quality. While recent Vision-Language Models (VLMs) demonstrate strong general visual understanding, their proficiency in comprehending the nuanced cinematic grammar embedded within individual shots remains largely unexplored and lacks robust evaluation. This critical gap limits both fine-grained visual comprehension and the precision of AI-assisted video generation. To address this, we introduce ShotBench, a comprehensive benchmark specifically designed for cinematic language understanding. It features over 3.5k expert-annotated QA pairs from images and video clips, meticulously curated from over 200 acclaimed (predominantly Oscar-nominated) films and spanning eight key cinematography dimensions. Our evaluation of 24 leading VLMs on ShotBench reveals their substantial limitations: even the top-performing model achieves less than 60% average accuracy, particularly struggling with fine-grained visual cues and complex spatial reasoning. To catalyze advancement in this domain, we construct ShotQA, a large-scale multimodal dataset comprising approximately 70k cinematic QA pairs. Leveraging ShotQA, we develop ShotVL through supervised fine-tuning and Group Relative Policy Optimization. ShotVL significantly outperforms all existing open-source and proprietary models on ShotBench, establishing new state-of-the-art performance. We open-source our models, data, and code to foster rapid progress in this crucial area of AI-driven cinematic understanding and generation.

Affordance grounding focuses on predicting the specific regions of objects that are associated with the actions to be performed by robots. It plays a vital role in the fields of human-robot interaction, human-object interaction, embodied manipulation, and embodied perception. Existing models often neglect the affordance shared among different objects because they lack the Chain-of-Thought(CoT) reasoning abilities, limiting their out-of-domain (OOD) generalization and explicit reasoning capabilities. To address these challenges, we propose Affordance-R1, the first unified affordance grounding framework that integrates cognitive CoT guided Group Relative Policy Optimization (GRPO) within a reinforcement learning paradigm. Specifically, we designed a sophisticated affordance function, which contains format, perception, and cognition rewards to effectively guide optimization directions. Furthermore, we constructed a high-quality affordance-centric reasoning dataset, ReasonAff, to support training. Trained exclusively via reinforcement learning with GRPO and without explicit reasoning data, Affordance-R1 achieves robust zero-shot generalization and exhibits emergent test-time reasoning capabilities. Comprehensive experiments demonstrate that our model outperforms well-established methods and exhibits open-world generalization. To the best of our knowledge, Affordance-R1 is the first to integrate GRPO-based RL with reasoning into affordance reasoning. The code of our method and our dataset is released on https://github.com/hq-King/Affordance-R1.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly with algorithms like Group Relative Policy Optimization (GRPO), has proven highly effective in enhancing the reasoning capabilities of large language models. However, a critical bottleneck in current pipelines lies in the limited diversity of sampled trajectories during group rollouts. Homogeneous trajectories and their associated rewards would diminish the return signals for policy updates, thereby hindering effective policy learning. This lack of diversity stems primarily from token-level stochastic sampling, where local variations are likely to collapse into near-identical reasoning paths. To address this limitation, we propose Lookahead Tree-Based Rollouts (LATR), a novel rollout strategy designed to explicitly promotes trajectory-level diversity by enforcing branching into different candidate tokens likely to yield distinct continuations. Specifically, LATR iteratively operates in three stages: (1) branching at high-uncertainty generation steps, (2) performing lookahead simulation for each new branch, and (3) pruning branches that exhibits prolonged similarity during simulation. Compared with stochastic Sampling, LATR accelerates policy learning by 131% on average and improves final pass@1 performance by 4.2% on both GRPO and Dynamic sAmpling Policy Optimization (DAPO) algorithms across different reasoning tasks. Our code and data are publicly available at https://github.com/starreeze/latr.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

As large language models (LLMs) are increasingly integrated into numerous applications across various domains, LLMs' safety becomes a critical concern for both application developers and intended users. Currently, great efforts have been made to develop safety benchmarks with fine-grained taxonomies. However, these benchmarks' taxonomies are disparate with different safety policies. Thus, existing safeguards trained on these benchmarks are either coarse-grained to only distinguish between safe and unsafe, or constrained by the narrow risk taxonomies of a single benchmark. To leverage these fine-grained safety taxonomies across multiple safety benchmarks, in this paper, we propose GSPR, a Generalizable Safety Policy Reasoner to identify unsafe input prompts and LLMs' outputs with violated safety taxonomies through Group Relative Policy Optimization (GRPO). Unlike prior safeguards which only cover a fixed set of risk factors, our GSPR incentivizes its reasoning capability with varied safety taxonomies through our careful cold-start strategy and reward design. Consequently, our GSPR can be trained across multiple safety benchmarks with distinct taxonomies and naturally exhibits powerful generalization ability. We conduct extensive experiments to show that our GSPR significantly improves existing safety guardrails' reasoning capabilities for both safety and category prediction tasks. Moreover, our GSPR not only demonstrates powerful safety generalization abilities but also achieves the least inference token costs with explanations.

Intent detection, a critical component in task-oriented dialogue (TOD) systems, faces significant challenges in adapting to the rapid influx of integrable tools with complex interrelationships. Existing approaches, such as zero-shot reformulations and LLM-based dynamic recognition, struggle with performance degradation when encountering unseen intents, leading to erroneous task routing. To enhance the model's generalization performance on unseen tasks, we employ Reinforcement Learning (RL) combined with a Reward-based Curriculum Sampling (RCS) during Group Relative Policy Optimization (GRPO) training in intent detection tasks. Experiments demonstrate that RL-trained models substantially outperform supervised fine-tuning (SFT) baselines in generalization. Besides, the introduction of the RCS, significantly bolsters the effectiveness of RL in intent detection by focusing the model on challenging cases during training. Moreover, incorporating Chain-of-Thought (COT) processes in RL notably improves generalization in complex intent detection tasks, underscoring the importance of thought in challenging scenarios. This work advances the generalization of intent detection tasks, offering practical insights for deploying adaptable dialogue systems.

The recent explosive interest in the reasoning capabilities of large language models, such as DeepSeek-R1, has demonstrated remarkable success through reinforcement learning-based fine-tuning frameworks, exemplified by methods like Group Relative Policy Optimization (GRPO). However, such reasoning abilities remain underexplored and notably absent in vision foundation models, including representation models like the DINO series. In this work, we propose DINO-R1, the first such attempt to incentivize visual in-context reasoning capabilities of vision foundation models using reinforcement learning. Specifically, DINO-R1 introduces Group Relative Query Optimization (GRQO), a novel reinforcement-style training strategy explicitly designed for query-based representation models, which computes query-level rewards based on group-normalized alignment quality. We also apply KL-regularization to stabilize the objectness distribution to reduce the training instability. This joint optimization enables dense and expressive supervision across queries while mitigating overfitting and distributional drift. Building upon Grounding-DINO, we train a series of DINO-R1 family models that integrate a visual prompt encoder and a visual-guided query selection mechanism. Extensive experiments on COCO, LVIS, and ODinW demonstrate that DINO-R1 significantly outperforms supervised fine-tuning baselines, achieving strong generalization in both open-vocabulary and closed-set visual prompting scenarios.

Recent advances in text-to-video generation have produced increasingly realistic and diverse content, yet evaluating such videos remains a fundamental challenge due to their multi-faceted nature encompassing visual quality, semantic alignment, and physical consistency. Existing evaluators and reward models are limited to single opaque scores, lack interpretability, or provide only coarse analysis, making them insufficient for capturing the comprehensive nature of video quality assessment. We present VideoScore2, a multi-dimensional, interpretable, and human-aligned framework that explicitly evaluates visual quality, text-to-video alignment, and physical/common-sense consistency while producing detailed chain-of-thought rationales. Our model is trained on a large-scale dataset VideoFeedback2 containing 27,168 human-annotated videos with both scores and reasoning traces across three dimensions, using a two-stage pipeline of supervised fine-tuning followed by reinforcement learning with Group Relative Policy Optimization (GRPO) to enhance analytical robustness. Extensive experiments demonstrate that VideoScore2 achieves superior performance with 44.35 (+5.94) accuracy on our in-domain benchmark VideoScore-Bench-v2 and 50.37 (+4.32) average performance across four out-of-domain benchmarks (VideoGenReward-Bench, VideoPhy2, etc), while providing interpretable assessments that bridge the gap between evaluation and controllable generation through effective reward modeling for Best-of-N sampling. Project Page: https://tiger-ai-lab.github.io/VideoScore2/

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly double-check their work after having derived the correct answer. To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved. Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO). LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process. Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression. Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs. Our code is released at https://github.com/zxiangx/LC-R1.

Vision-Language-Action (VLA) models aim to unify perception, language understanding, and action generation, offering strong cross-task and cross-scene generalization with broad impact on embodied AI. However, current VLA models often lack explicit step-by-step reasoning, instead emitting final actions without considering affordance constraints or geometric relations. Their post-training pipelines also rarely reinforce reasoning quality, relying primarily on supervised fine-tuning with weak reward design. To address these challenges, we present VLA-R1, a reasoning-enhanced VLA that integrates Reinforcement Learning from Verifiable Rewards (RLVR) with Group Relative Policy Optimization (GRPO) to systematically optimize both reasoning and execution. Specifically, we design an RLVR-based post-training strategy with verifiable rewards for region alignment, trajectory consistency, and output formatting, thereby strengthening reasoning robustness and execution accuracy. Moreover, we develop VLA-CoT-13K, a high-quality dataset that provides chain-of-thought supervision explicitly aligned with affordance and trajectory annotations. Furthermore, extensive evaluations on in-domain, out-of-domain, simulation, and real-robot platforms demonstrate that VLA-R1 achieves superior generalization and real-world performance compared to prior VLA methods. We plan to release the model, code, and dataset following the publication of this work. Code: https://github.com/GigaAI-research/VLA-R1. Website: https://gigaai-research.github.io/VLA-R1.

Recent advances in post-training techniques have endowed Large Language Models (LLMs) with enhanced capabilities for tackling complex, logic-intensive tasks through the generation of supplementary planning tokens. This development raises a fundamental question: Are these models aware of what they "learn" and "think"? To address this, we define three core competencies: (1) awareness of learned latent policies, (2) generalization of these policies across domains, and (3) alignment between internal reasoning traces and final outputs. We empirically evaluate these abilities on several tasks, each designed to require learning a distinct policy. Furthermore, we contrast the profiles of models post-trained via Supervised Fine-Tuning (SFT), Direct Policy Optimization (DPO), and Group Relative Policy Optimization (GRPO). Our findings indicate that RL-trained models not only demonstrate greater awareness of their learned behaviors and stronger generalizability to novel, structurally similar tasks than SFT models but also often exhibit weak alignment between their reasoning traces and final outputs, an effect most pronounced in GRPO-trained models.

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a novel CoT compression framework based on step entropy, a metric that quantifies the informational contribution of individual reasoning steps to identify redundancy. Through theoretical analysis and extensive empirical validation on mathematical reasoning benchmarks, we demonstrate that steps with low entropy are indeed highly redundant. Our experiments reveal that an astonishing 80\% of low-entropy intermediate steps can be pruned with minor degradation in the final answer accuracy across DeepSeek-R1-7B, 14B and Qwen3-8B. This finding sharply contrasts with random or high-entropy pruning, which severely impairs reasoning performance. Building on this, we propose a novel two-stage training strategy combining Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO) reinforcement learning. This approach enables LLMs to autonomously learn to generate compressed COTs during inference by strategically incorporating [SKIP] tokens. Our method significantly enhances LLM inference efficiency while rigorously preserving accuracy, offering profound implications for practical LLM deployment and a deeper understanding of reasoning structures.

Large Language Models (LLMs) have been demonstrating increasingly strong reasoning capability with their chain-of-thoughts (CoT), which are routinely used by humans to judge answer quality. This reliance creates a powerful yet fragile basis for trust. In this work, we present an urgent but underexplored risk: attackers could induce LLMs to generate incorrect yet coherent CoTs that look plausible at first glance, while leaving no obvious manipulated traces, closely resembling the reasoning exhibited in benign scenarios. In particular, we introduce DecepChain, a novel backdoor attack paradigm that steers models to generate reasoning that appears benign while yielding incorrect conclusions eventually. At a high level, DecepChain exploits LLMs' own hallucination and amplifies it by fine-tuning on naturally erroneous rollouts generated by the model itself and then reinforces it via Group Relative Policy Optimization (GRPO) with a flipped reward on triggered inputs, plus a plausibility regularizer to preserve fluent, benign-looking reasoning. Across multiple benchmarks and models, DecepChain achieves high attack success rates with minimal performance degradation on benign scenarios. Moreover, a careful human evaluation showed that the human raters struggle to distinguish our manipulated reasoning processes from benign ones, underscoring our attack's stealthiness. Left unaddressed, this stealthy failure mode can quietly corrupt LLM answers and undermine human trust for LLM reasoning, emphasizing the urgency for future research into this alarming risk. Project page: https://decepchain.github.io/.

The ability of large language models (LLMs) to process and reason over long textual inputs is critical for a wide range of real-world applications. However, progress in this area is significantly constrained by the absence of high-quality, diverse, and verifiable long-context datasets suitable for both training and evaluation. This work introduces a modular, extensible framework for synthetic long-context data generation via prompt-based interaction with LLMs. The framework supports multiple training and alignment objectives, including Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and Group Relative Policy Optimization (GRPO). It encompasses four core generation paradigms: multi-turn conversational dialogues, document-grounded input-output pairs, verifiable instruction-response tasks, and long-context reasoning examples. Through templated prompting, a model-agnostic architecture, and metadata-enriched outputs, the proposed approach facilitates scalable, controllable, and purpose-aligned dataset creation for advancing long-context capabilities in LLMs.

Enhancing the spatial reasoning capabilities of Multi-modal Large Language Models (MLLMs) for video understanding is crucial yet challenging. We present Spatial-R1, a targeted approach involving two key contributions: the curation of SR, a new video spatial reasoning dataset from ScanNet with automatically generated QA pairs across seven task types, and the application of Task-Specific Group Relative Policy Optimization (GRPO) for fine-tuning. By training the Qwen2.5-VL-7B-Instruct model on SR using GRPO, Spatial-R1 significantly advances performance on the VSI-Bench benchmark, achieving a 7.4\% gain over the baseline and outperforming strong contemporary models. This work validates the effectiveness of specialized data curation and optimization techniques for improving complex spatial reasoning in video MLLMs.

Kernel development in deep learning requires optimizing computational units across hardware while balancing memory management, parallelism, and hardware-specific optimizations through extensive empirical tuning. Although domain-specific languages like Triton simplify GPU programming by abstracting low-level details, developers must still manually tune critical parameters such as tile sizes and memory access patterns through iterative experimentation, creating substantial barriers to optimal performance and wider adoption. In this work, we introduce AutoTriton, the first model dedicated to Triton programming powered by reinforcement learning (RL). AutoTriton performs supervised fine-tuning (SFT) to be equipped with essential Triton programming expertise using a high-quality data gathering pipeline, and conducts RL with Group Relative Policy Optimization (GRPO) algorithm, combining a rule-based reward and an execution-based reward to further improve Triton programming ability, sequentially. Experiments across five evaluation channels of TritonBench and KernelBench illustrate that our 8B model AutoTriton achieves performance comparable to mainstream large models, including Claude-4-Sonnet and DeepSeek-R1-0528. Further experimental analysis demonstrates the crucial role of each module within AutoTriton, including the SFT stage, the RL stage, and the reward design strategy. These findings underscore the promise of RL for automatically generating high-performance kernels, and since high-performance kernels are core components of AI systems, this breakthrough establishes an important foundation for building more efficient AI systems. The model and code will be available at https://github.com/AI9Stars/AutoTriton.

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness. In this study, we identify a critical yet underexplored issue in RL training: low-probability tokens disproportionately influence model updates due to their large gradient magnitudes. This dominance hinders the effective learning of high-probability tokens, whose gradients are essential for LLMs' performance but are substantially suppressed. To mitigate this interference, we propose two novel methods: Advantage Reweighting and Low-Probability Token Isolation (Lopti), both of which effectively attenuate gradients from low-probability tokens while emphasizing parameter updates driven by high-probability tokens. Our approaches promote balanced updates across tokens with varying probabilities, thereby enhancing the efficiency of RL training. Experimental results demonstrate that they substantially improve the performance of GRPO-trained LLMs, achieving up to a 46.2% improvement in K&K Logic Puzzle reasoning tasks. Our implementation is available at https://github.com/zhyang2226/AR-Lopti.

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

Text-to-image (T2I) generation has achieved remarkable progress in instruction following and aesthetics. However, a persistent challenge is the prevalence of physical artifacts, such as anatomical and structural flaws, which severely degrade perceptual quality and limit application. Given the diversity and complexity of these artifacts, a systematic and fine-grained evaluation framework is required, which is lacking in current benchmarks. To fill this gap, we introduce MagicMirror, a comprehensive framework for artifacts assessment. We first establish a detailed taxonomy of generated image artifacts. Guided by this taxonomy, we manually annotate MagicData340K, the first human-annotated large-scale dataset of 340K generated images with fine-grained artifact labels. Building on this dataset, we train MagicAssessor, a Vision-Language Model (VLM) that provides detailed assessments and corresponding labels. To overcome challenges like class imbalance and reward hacking, we design a novel data sampling strategy and a multi-level reward system for Group Relative Policy Optimization (GRPO). Finally, we leverage MagicAssessor to construct MagicBench, an automated benchmark for evaluating the image artifacts of current T2I models. Our evaluation with MagicBench reveals that despite their widespread adoption, even top-tier models like GPT-image-1 are consistently plagued by significant artifacts, highlighting artifact reduction as a critical frontier for future T2I development. Project page: https://wj-inf.github.io/MagicMirror-page/.

The rapid progress of large language models (LLMs) has sparked growing interest in building Artificial General Intelligence (AGI) within Graphical User Interface (GUI) environments. However, existing GUI agents based on LLMs or vision-language models (VLMs) often fail to generalize to novel environments and rely heavily on manually curated, diverse datasets. To overcome these limitations, we introduce ScreenExplorer, a VLM trained via Group Relative Policy Optimization(GRPO) in real, dynamic, and open-ended GUI environments. Innovatively, we introduced a world-model-based curiosity reward function to help the agent overcome the cold-start phase of exploration. Additionally, distilling experience streams further enhances the model's exploration capabilities. Our training framework enhances model exploration in open GUI environments, with trained models showing better environmental adaptation and sustained exploration compared to static deployment models. Our findings offer a scalable pathway toward AGI systems with self-improving capabilities in complex interactive settings.

Game playing has long served as a fundamental benchmark for evaluating Artificial General Intelligence (AGI). While Large Language Models (LLMs) have demonstrated impressive capabilities in general reasoning, their effectiveness in spatial strategic reasoning, which is critical for complex and fully observable board games, remains insufficiently explored. In this work, we adopt Chinese Chess (Xiangqi) as a challenging and rich testbed due to its intricate rules and spatial complexity. To advance LLMs' strategic competence in such environments, we propose a training framework tailored to Xiangqi, built upon a large-scale dataset of five million board-move pairs enhanced with expert annotations and engine evaluations. Building on this foundation, we introduce Xiangqi-R1, a 7B-parameter model trained in multi-stage manner: (1) fine-tuning for legal move prediction to capture basic spatial rules, (2) incorporating strategic annotations to improve decision-making, and (3) applying reinforcement learning via Group Relative Policy Optimization (GRPO) with multi-dimensional reward signals to enhance reasoning stability. Our Experimental results indicate that, despite their size and power, general-purpose LLMs struggle to achieve satisfactory performance in these tasks. Compared to general-purpose LLMs, Xiangqi-R1 greatly advances with an 18% rise in move legality and a 22% boost in analysis accuracy. Our results point to a promising path for creating general strategic intelligence in spatially complex areas.

LLM-based search agents are increasingly trained on entity-centric synthetic data to solve complex, knowledge-intensive tasks. However, prevailing training methods like Group Relative Policy Optimization (GRPO) discard this rich entity information, relying instead on sparse, outcome-based rewards. This critical limitation renders them unable to distinguish informative "near-miss" samples-those with substantially correct reasoning but a flawed final answer-from complete failures, thus discarding valuable learning signals. We address this by leveraging the very entities discarded during training. Our empirical analysis reveals a strong positive correlation between the number of ground-truth entities identified during an agent's reasoning process and final answer accuracy. Building on this insight, we introduce Entity-aware Group Relative Policy Optimization (E-GRPO), a novel framework that formulates a dense entity-aware reward function. E-GRPO assigns partial rewards to incorrect samples proportional to their entity match rate, enabling the model to effectively learn from these "near-misses". Experiments on diverse question-answering (QA) and deep research benchmarks show that E-GRPO consistently and significantly outperforms the GRPO baseline. Furthermore, our analysis reveals that E-GRPO not only achieves superior accuracy but also induces more efficient reasoning policies that require fewer tool calls, demonstrating a more effective and sample-efficient approach to aligning search agents.

Recent advancements in reinforcement learning have significantly advanced the reasoning capabilities of multimodal large language models (MLLMs). While approaches such as Group Relative Policy Optimization (GRPO) and rule-based reward mechanisms demonstrate promise in text and image domains, their application to video understanding remains limited. This paper presents a systematic exploration of Reinforcement Fine-Tuning (RFT) with GRPO for video MLLMs, aiming to enhance spatio-temporal perception while maintaining general capabilities. Our experiments reveal that RFT is highly data-efficient for task-specific improvements. Through multi-task RFT on spatio-temporal perception objectives with limited samples, we develop VideoChat-R1, a powerful video MLLM that achieves state-of-the-art performance on spatio-temporal perception tasks without sacrificing chat ability, while exhibiting emerging spatio-temporal reasoning abilities. Compared to Qwen2.5-VL-7B, VideoChat-R1 boosts performance several-fold in tasks like temporal grounding (+31.8) and object tracking (+31.2). Additionally, it significantly improves on general QA benchmarks such as VideoMME (+0.9), MVBench (+1.0), and Perception Test (+0.9). Our findings underscore the potential of RFT for specialized task enhancement of Video MLLMs. We hope our work offers valuable insights for future RL research in video MLLMs.

Multimodal reasoning over long-horizon video is challenging due to the need for precise spatiotemporal fusion and alignment across modalities. While recent methods such as Group Relative Policy Optimization (GRPO) have shown promise in this domain, they suffer from three key limitations: (1) data inefficiency from their on-policy design, (2) a vanishing advantage problem, where identical or near-identical rewards within a group eliminate the learning signal by producing zero-valued advantages, and (3) uniform credit assignment that fails to emphasize critical reasoning steps. We introduce AVATAR (Audio-Video Agent for Alignment and Reasoning), a framework that addresses these limitations through two core components: (1) an off-policy training architecture that improves sample efficiency and resolves vanishing advantages by reusing past experiences with greater reward diversity, and (2) Temporal Advantage Shaping (TAS), a novel credit assignment strategy that upweights key reasoning phases during learning. AVATAR achieves strong performance across various benchmarks, outperforming the Qwen2.5-Omni baseline by +5.4on MMVU, +4.9 on OmniBench, and +4.5 on Video-Holmes, while demonstrating over 35% higher sample efficiency.

As autonomous agents become adept at understanding and interacting with graphical user interface (GUI) environments, a new era of automated task execution is emerging. Recent studies have demonstrated that Reinforcement Learning (RL) can effectively enhance agents' performance in dynamic interactive GUI environments. However, these methods face two key limitations: (1) they overlook the significant variation in difficulty across different GUI tasks by treating the entire training data as a uniform set, which hampers the agent's ability to adapt its learning process; and (2) most approaches collapse task-specific nuances into a single, coarse reward, leaving the agent with a uniform signal that yields inefficient policy updates. To address these limitations, we propose CRAFT-GUI, a curriculum learning framework based on Group Relative Policy Optimization (GRPO) that explicitly accounts for the varying difficulty across trajectories. To enable more fine-grained policy optimization, we design a reward function that combines simple rule-based signals with model-judged evaluation, providing richer and more nuanced feedback during training. Experimental results demonstrate that our method achieves significant improvements over previous state-of-the-art approaches, outperforming them by 5.6% on public benchmarks Android Control and 10.3% on our internal online benchmarks, respectively. These findings empirically validate the effectiveness of integrating reinforcement learning with curriculum learning in GUI interaction tasks.

Recent works have demonstrated the effectiveness of reinforcement learning (RL)-based post-training in enhancing the reasoning capabilities of large language models (LLMs). In particular, Group Relative Policy Optimization (GRPO) has shown impressive success by employing a PPO-style reinforcement algorithm with group-based normalized rewards. However, the application of GRPO to Video Large Language Models (Video LLMs) has been less studied. In this paper, we explore GRPO for video LLMs and identify two primary issues that impede its effective learning: (1) reliance on safeguards, and (2) the vanishing advantage problem. To mitigate these challenges, we propose DeepVideo-R1, a video large language model trained with our proposed Reg-GRPO (Regressive GRPO) and difficulty-aware data augmentation strategy. Reg-GRPO reformulates the GRPO objective as a regression task, directly predicting the advantage in GRPO. This design eliminates the need for safeguards like clipping and min functions, thereby facilitating more direct policy guidance by aligning the model with the advantage values. We also design the difficulty-aware data augmentation strategy that dynamically augments training samples at solvable difficulty levels, fostering diverse and informative reward signals. Our comprehensive experiments show that DeepVideo-R1 significantly improves video reasoning performance across multiple video reasoning benchmarks.

This work revisits the dominant supervised fine-tuning (SFT) then reinforcement learning (RL) paradigm for training Large Vision-Language Models (LVLMs), and reveals a key finding: SFT can significantly undermine subsequent RL by inducing ``pseudo reasoning paths'' imitated from expert models. While these paths may resemble the native reasoning paths of RL models, they often involve prolonged, hesitant, less informative steps, and incorrect reasoning. To systematically study this effect, we introduce VLAA-Thinking, a new multimodal dataset designed to support reasoning in LVLMs. Constructed via a six-step pipeline involving captioning, reasoning distillation, answer rewrite and verification, VLAA-Thinking comprises high-quality, step-by-step visual reasoning traces for SFT, along with a more challenging RL split from the same data source. Using this dataset, we conduct extensive experiments comparing SFT, RL and their combinations. Results show that while SFT helps models learn reasoning formats, it often locks aligned models into imitative, rigid reasoning modes that impede further learning. In contrast, building on the Group Relative Policy Optimization (GRPO) with a novel mixed reward module integrating both perception and cognition signals, our RL approach fosters more genuine, adaptive reasoning behavior. Notably, our model VLAA-Thinker, based on Qwen2.5VL 3B, achieves top-1 performance on Open LMM Reasoning Leaderboard (https://huggingface.co/spaces/opencompass/Open_LMM_Reasoning_Leaderboard) among 4B scale LVLMs, surpassing the previous state-of-the-art by 1.8%. We hope our findings provide valuable insights in developing reasoning-capable LVLMs and can inform future research in this area.

Large reasoning models (LRM) with long chain-of-thought (CoT) capabilities have shown strong performance on objective tasks, such as math reasoning and coding. However, their effectiveness on subjective questions that may have different responses from different perspectives is still limited by a tendency towards homogeneous reasoning, introduced by the reliance on a single ground truth in supervised fine-tuning and verifiable reward in reinforcement learning. Motivated by the finding that increasing role perspectives consistently improves performance, we propose MultiRole-R1, a diversity-enhanced framework with multiple role perspectives, to improve the accuracy and diversity in subjective reasoning tasks. MultiRole-R1 features an unsupervised data construction pipeline that generates reasoning chains that incorporate diverse role perspectives. We further employ reinforcement learning via Group Relative Policy Optimization (GRPO) with reward shaping, by taking diversity as a reward signal in addition to the verifiable reward. With specially designed reward functions, we successfully promote perspective diversity and lexical diversity, uncovering a positive relation between reasoning diversity and accuracy. Our experiment on six benchmarks demonstrates MultiRole-R1's effectiveness and generalizability in enhancing both subjective and objective reasoning, showcasing the potential of diversity-enhanced training in LRMs.

Reinforcement learning has been widely applied to enhance the reasoning capabilities of large language models. Extending the inference limits of smaller models has become a prominent research focus. However, algorithms such as Group Relative Policy Optimization (GRPO) suffer from a clear drawback: the upper bound of a model's rollout responses is entirely determined by the model itself, preventing the acquisition of knowledge from samples that are either all incorrect or all correct. In this paper, we introduce Group Contrastive Policy Optimization (GCPO), a method that incorporates external standard reference answers. When the model cannot solve a problem, the reference answer supplies the correct response, steering the model toward an unequivocally accurate update direction. This approach offers two main advantages: (1) it improves training efficiency by fully utilizing every sample; (2) it enables the model to emulate the problem solving strategy of the reference answer during training, thereby enhancing generalization in reasoning. GCPO achieves outstanding results across multiple benchmark datasets, yielding substantial improvements over the baseline model. Our code is available at: https://github.com/AchoWu/GCPO.

Recent advances in reinforcement learning for language model post-training, such as Group Relative Policy Optimization (GRPO), have shown promise in low-resource settings. However, GRPO typically relies on solution-level and scalar reward signals that fail to capture the semantic diversity among sampled completions. This leads to what we identify as a diversity-quality inconsistency, where distinct reasoning paths may receive indistinguishable rewards. To address this limitation, we propose Diversity-aware Reward Adjustment (DRA), a method that explicitly incorporates semantic diversity into the reward computation. DRA uses Submodular Mutual Information (SMI) to downweight redundant completions and amplify rewards for diverse ones. This encourages better exploration during learning, while maintaining stable exploitation of high-quality samples. Our method integrates seamlessly with both GRPO and its variant DR.~GRPO, resulting in DRA-GRPO and DGA-DR.~GRPO. We evaluate our method on five mathematical reasoning benchmarks and find that it outperforms recent strong baselines. It achieves state-of-the-art performance with an average accuracy of 58.2%, using only 7,000 fine-tuning samples and a total training cost of approximately $55. The code is available at https://github.com/xiwenc1/DRA-GRPO.

Building agents that autonomously operate mobile devices has attracted increasing attention. While Vision-Language Models (VLMs) show promise, most existing approaches rely on direct state-to-action mappings, which lack structured reasoning and planning, and thus generalize poorly to novel tasks or unseen UI layouts. We introduce Hi-Agent, a trainable hierarchical vision-language agent for mobile control, featuring a high-level reasoning model and a low-level action model that are jointly optimized. For efficient training, we reformulate multi-step decision-making as a sequence of single-step subgoals and propose a foresight advantage function, which leverages execution feedback from the low-level model to guide high-level optimization. This design alleviates the path explosion issue encountered by Group Relative Policy Optimization (GRPO) in long-horizon tasks and enables stable, critic-free joint training. Hi-Agent achieves a new State-Of-The-Art (SOTA) 87.9% task success rate on the Android-in-the-Wild (AitW) benchmark, significantly outperforming prior methods across three paradigms: prompt-based (AppAgent: 17.7%), supervised (Filtered BC: 54.5%), and reinforcement learning-based (DigiRL: 71.9%). It also demonstrates competitive zero-shot generalization on the ScreenSpot-v2 benchmark. On the more challenging AndroidWorld benchmark, Hi-Agent also scales effectively with larger backbones, showing strong adaptability in high-complexity mobile control scenarios.

Aligning large language models (LLMs) with human values and safety constraints is challenging, especially when objectives like helpfulness, truthfulness, and avoidance of harm conflict. Reinforcement Learning from Human Feedback (RLHF) has achieved notable success in steering models, but is complex and can be unstable. Recent approaches such as Direct Preference Optimization (DPO) simplify preference-based fine-tuning but may introduce bias or trade-off certain objectives~dpo. In this work, we propose a Group Relative Policy Optimization (GRPO) framework with a multi-label reward regression model to achieve safe and aligned language generation. The GRPO algorithm optimizes a policy by comparing groups of sampled responses, eliminating the need for a separate value critic and improving training efficiency~grpo. We train a reward model to predict multiple alignment scores (e.g., safety, helpfulness, etc.), which are combined into a single reward signal. We provide a theoretical derivation for using this learned multi-aspect reward within GRPO and discuss its advantages and limitations. Empirically, our approach improves all the safety and quality metrics evaluated in language generation tasks on model scales (0.5B, 7B, and 14B parameters), demonstrating a robust balance of objectives. We compare GRPO to PPO-based RLHF and DPO, highlighting that GRPO achieves alignment with significantly lower computational cost and explicit multi-objective handling. \textbf{We will open-source all trained models at https://huggingface.co/hydroxai.

Large Language Models (LLMs) have demonstrated impressive capabilities in language processing, yet they often struggle with tasks requiring genuine visual spatial reasoning. In this paper, we introduce a novel two-stage training framework designed to equip standard LLMs with visual reasoning abilities for maze navigation. First, we leverage Supervised Fine Tuning (SFT) on a curated dataset of tokenized maze representations to teach the model to predict step-by-step movement commands. Next, we apply Group Relative Policy Optimization (GRPO)-a technique used in DeepSeekR1-with a carefully crafted reward function to refine the model's sequential decision-making and encourage emergent chain-of-thought behaviors. Experimental results on synthetically generated mazes show that while a baseline model fails to navigate the maze, the SFT-trained model achieves 86% accuracy, and further GRPO fine-tuning boosts accuracy to 93%. Qualitative analyses reveal that GRPO fosters more robust and self-corrective reasoning, highlighting the potential of our approach to bridge the gap between language models and visual spatial tasks. These findings offer promising implications for applications in robotics, autonomous navigation, and other domains that require integrated visual and sequential reasoning.

Recent advancements in reinforcement learning, particularly through Group Relative Policy Optimization (GRPO), have significantly improved multimodal large language models for complex reasoning tasks. However, two critical limitations persist: 1) they often produce unfocused, verbose reasoning chains that obscure salient spatiotemporal cues and 2) binary rewarding fails to account for partially correct answers, resulting in high reward variance and inefficient learning. In this paper, we propose TW-GRPO, a novel framework that enhances visual reasoning with focused thinking and dense reward granularity. Specifically, we employs a token weighting mechanism that prioritizes tokens with high informational density (estimated by intra-group variance), suppressing redundant tokens like generic reasoning prefixes. Furthermore, we reformulate RL training by shifting from single-choice to multi-choice QA tasks, where soft rewards enable finer-grained gradient estimation by distinguishing partial correctness. Additionally, we propose question-answer inversion, a data augmentation strategy to generate diverse multi-choice samples from existing benchmarks. Experiments demonstrate state-of-the-art performance on several video reasoning and general understanding benchmarks. Notably, TW-GRPO achieves 50.4\% accuracy on CLEVRER (18.8\% improvement over Video-R1) and 65.8\% on MMVU. Our codes are available at https://github.com/longmalongma/TW-GRPO.

Understanding and recognizing human-object interaction (HOI) is a pivotal application in AR/VR and robotics. Recent open-vocabulary HOI detection approaches depend exclusively on large language models for richer textual prompts, neglecting their inherent 3D spatial understanding capabilities. To address this shortcoming, we introduce HOID-R1, the first HOI detection framework that integrates chain-of-thought (CoT) guided supervised fine-tuning (SFT) with group relative policy optimization (GRPO) within a reinforcement learning (RL) paradigm. Specifically, we initially apply SFT to imbue the model with essential reasoning capabilities, forcing the model to articulate its thought process in the output. Subsequently, we integrate GRPO to leverage multi-reward signals for policy optimization, thereby enhancing alignment across diverse modalities. To mitigate hallucinations in the CoT reasoning, we introduce an "MLLM-as-a-judge" mechanism that supervises the CoT outputs, further improving generalization. Extensive experiments show that HOID-R1 achieves state-of-the-art performance on HOI detection benchmarks and outperforms existing methods in open-world generalization to novel scenarios.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

The video reasoning ability of multimodal large language models (MLLMs) is crucial for downstream tasks like video question answering and temporal grounding. While recent approaches have explored text-based chain-of-thought (CoT) reasoning for MLLMs, these methods often suffer from limited cross-modal interaction and increased hallucination, especially with longer videos or reasoning chains. To address these challenges, we propose Video Intelligence via Tool-Augmented Learning (VITAL), a novel end-to-end agentic video reasoning framework. With a visual toolbox, the model can densely sample new video frames on demand and generate multimodal CoT for precise long video reasoning. We observe that temporal grounding and question answering are mutually beneficial for video understanding tasks. Therefore, we construct two high-quality multi-task video reasoning datasets MTVR-CoT-72k for supervised fine-tuning and MTVR-RL-110k for reinforcement learning. Moreover, we propose a Difficulty-aware Group Relative Policy Optimization algorithm (DGRPO) to mitigate difficulty imbalance in multi-task reinforcement learning. Extensive experiments on 11 challenging video understanding benchmarks demonstrate the advanced reasoning ability of VITAL, outperforming existing methods in video question answering and temporal grounding tasks, especially in long video scenarios. All code, data and model weight will be made publicly available.

Large language models (LLMs) are reshaping the recommender system paradigm by enabling users to express preferences and receive recommendations through conversations. Yet, aligning LLMs to the recommendation task remains challenging: pretrained LLMs often generate out-of-catalog items, violate required output formats, and their ranking quality degrades sharply toward the end of the generated list. To this end, we propose ConvRec-R1, a two-stage framework for end-to-end training of LLM-based conversational recommender systems. In Stage 1, we construct a behavioral-cloning dataset with a Remap-Reflect-Adjust pipeline, which produces high-quality, catalog-grounded demonstrations from powerful blackbox LLMs to warm-start the RL training. In Stage 2, we propose Rank-GRPO, a principled extension of group relative policy optimization (GRPO) tailored to tasks with rank-style outputs. Rank-GRPO treats each rank in the recommendation list as the unit instead of token (too fine-grained) or sequence (too coarse), redefining rewards to remove non-causal credit assignment and introducing a rank-level importance ratio based on the geometric mean of rank-wise token probabilities to stabilize policy updates. Experiments on the public Reddit-v2 dataset show that ConvRec-R1 converges faster and achieves higher Recall and NDCG than GRPO-style baselines. Code and datasets are released at https://github.com/yaochenzhu/Rank-GRPO.

Reinforcement Learning (RL) can directly enhance the reasoning capabilities of large language models without extensive reliance on Supervised Fine-Tuning (SFT). In this work, we revisit the traditional Policy Gradient (PG) mechanism and propose a minimalist RL approach termed Group Policy Gradient (GPG). Unlike conventional methods, GPG directly optimize the original RL objective, thus obviating the need for surrogate loss functions. As illustrated in our paper, by eliminating both the critic and reference models, and avoiding KL divergence constraints, our approach significantly simplifies the training process when compared to Group Relative Policy Optimization (GRPO). Our approach achieves superior performance without relying on auxiliary techniques or adjustments. Extensive experiments demonstrate that our method not only reduces computational costs but also consistently outperforms GRPO across various unimodal and multimodal tasks. Our code is available at https://github.com/AMAP-ML/GPG.

Tool-augmented language models have demonstrated strong capabilities, but their reliance on live API access creates scalability and reliability challenges during training and deployment. We propose MTR, a simulation-first training framework for tool-augmented reasoning. Instead of relying on live APIs, MTR learns from complete ReAct traces with schema-validated, simulated observations. Our approach operates through a multi-agent architecture where a ToolMaker generates task-specific, OpenAI-compatible tool interfaces, an AutoAgent produces structured think-act-observe sequences, and a ToolActor simulates realistic responses. Training proceeds in two stages: Stage-1 Supervised Fine-Tuning (SFT) teaches 'trace grammar' from complete reasoning sequences; Stage-2 Group Relative Policy Optimization (GRPO) optimizes strategy with a composite trace reward that balances answer correctness and internal consistency. Across four multi-hop QA benchmarks (HotpotQA, MuSiQue, 2WikiMultiHopQA, Bamboogle), MTR attains competitive Exact Match (EM) scores to live-API systems and excels on reasoning-intensive tasks, suggesting that effective tool reasoning can be learned from structured traces without live interactions.

The integration of large language models (LLMs) into education presents unprecedented opportunities for scalable personalized learning. However, standard LLMs often function as generic information providers, lacking alignment with fundamental pedagogical principles such as helpfulness, student-centered personalization, and creativity cultivation. To bridge this gap, we propose EduAlign, a novel framework designed to guide LLMs toward becoming more effective and responsible educational assistants. EduAlign consists of two main stages. In the first stage, we curate a dataset of 8k educational interactions and annotate them-both manually and automatically-along three key educational dimensions: Helpfulness, Personalization, and Creativity (HPC). These annotations are used to train HPC-RM, a multi-dimensional reward model capable of accurately scoring LLM outputs according to these educational principles. We further evaluate the consistency and reliability of this reward model. In the second stage, we leverage HPC-RM as a reward signal to fine-tune a pre-trained LLM using Group Relative Policy Optimization (GRPO) on a set of 2k diverse prompts. We then assess the pre- and post-finetuning models on both educational and general-domain benchmarks across the three HPC dimensions. Experimental results demonstrate that the fine-tuned model exhibits significantly improved alignment with pedagogical helpfulness, personalization, and creativity stimulation. This study presents a scalable and effective approach to aligning LLMs with nuanced and desirable educational traits, paving the way for the development of more engaging, pedagogically aligned AI tutors.

Image quality assessment (IQA) focuses on the perceptual visual quality of images, playing a crucial role in downstream tasks such as image reconstruction, compression, and generation. The rapid advancement of multi-modal large language models (MLLMs) has significantly broadened the scope of IQA, moving toward comprehensive image quality understanding that incorporates content analysis, degradation perception, and comparison reasoning beyond mere numerical scoring. Previous MLLM-based methods typically either generate numerical scores lacking interpretability or heavily rely on supervised fine-tuning (SFT) using large-scale annotated datasets to provide descriptive assessments, limiting their flexibility and applicability. In this paper, we propose Q-Insight, a reinforcement learning-based model built upon group relative policy optimization (GRPO), which demonstrates strong visual reasoning capability for image quality understanding while requiring only a limited amount of rating scores and degradation labels. By jointly optimizing score regression and degradation perception tasks with carefully designed reward functions, our approach effectively exploits their mutual benefits for enhanced performance. Extensive experiments demonstrate that Q-Insight substantially outperforms existing state-of-the-art methods in both score regression and degradation perception tasks, while exhibiting impressive zero-shot generalization to comparison reasoning tasks. Code will be available at https://github.com/lwq20020127/Q-Insight.

Chain-of-Thought (CoT) is a robust approach for tackling LLM tasks that require intermediate reasoning steps prior to generating a final answer. In this paper, we present GreenMind-Medium-14B-R1, the Vietnamese reasoning model inspired by the finetuning strategy based on Group Relative Policy Optimization. We also leverage a high-quality Vietnamese synthesized reasoning dataset and design two reward functions to tackle the main limitations of this technique: (i) language mixing, where we explicitly detect the presence of biased language characters during the process of sampling tokens, and (ii) we leverage Sentence Transformer-based models to ensure that the generated reasoning content maintains factual correctness and does not distort the final output. Experimental results on the Vietnamese dataset from the VLSP 2023 Challenge demonstrate that our model outperforms prior works and enhances linguistic consistency in its responses. Furthermore, we extend our evaluation to SeaExam-a multilingual multiple-choice dataset, showing the effectiveness of our reasoning method compared to few-shot prompting techniques.

Current research on Multimodal Retrieval-Augmented Generation (MRAG) enables diverse multimodal inputs but remains limited to single-modality outputs, restricting expressive capacity and practical utility. In contrast, real-world applications often demand both multimodal inputs and multimodal outputs for effective communication and grounded reasoning. Motivated by the recent success of Reinforcement Learning (RL) in complex reasoning tasks for Large Language Models (LLMs), we adopt RL as a principled and effective paradigm to address the multi-step, outcome-driven challenges inherent in multimodal output generation. Here, we introduce M2IO-R1, a novel framework for Multimodal Retrieval-Augmented Multimodal Generation (MRAMG) that supports both multimodal inputs and outputs. Central to our framework is an RL-based inserter, Inserter-R1-3B, trained with Group Relative Policy Optimization to guide image selection and placement in a controllable and semantically aligned manner. Empirical results show that our lightweight 3B inserter achieves strong reasoning capabilities with significantly reduced latency, outperforming baselines in both quality and efficiency.

In the age of powerful AI-generated text, automatic detectors have emerged to identify machine-written content. This poses a threat to author privacy and freedom, as text authored with AI assistance may be unfairly flagged. We propose AuthorMist, a novel reinforcement learning-based system to transform AI-generated text into human-like writing. AuthorMist leverages a 3-billion-parameter language model as a backbone, fine-tuned with Group Relative Policy Optimization (GPRO) to paraphrase text in a way that evades AI detectors. Our framework establishes a generic approach where external detector APIs (GPTZero, WinstonAI, Originality.ai, etc.) serve as reward functions within the reinforcement learning loop, enabling the model to systematically learn outputs that these detectors are less likely to classify as AI-generated. This API-as-reward methodology can be applied broadly to optimize text against any detector with an accessible interface. Experiments on multiple datasets and detectors demonstrate that AuthorMist effectively reduces the detectability of AI-generated text while preserving the original meaning. Our evaluation shows attack success rates ranging from 78.6% to 96.2% against individual detectors, significantly outperforming baseline paraphrasing methods. AuthorMist maintains high semantic similarity (above 0.94) with the original text while successfully evading detection. These results highlight limitations in current AI text detection technologies and raise questions about the sustainability of the detection-evasion arms race.

Recent advancements in Vision-Language-Action (VLA) models have shown promise for end-to-end autonomous driving by leveraging world knowledge and reasoning capabilities. However, current VLA models often struggle with physically infeasible action outputs, complex model structures, or unnecessarily long reasoning. In this paper, we propose AutoVLA, a novel VLA model that unifies reasoning and action generation within a single autoregressive generation model for end-to-end autonomous driving. AutoVLA performs semantic reasoning and trajectory planning directly from raw visual inputs and language instructions. We tokenize continuous trajectories into discrete, feasible actions, enabling direct integration into the language model. For training, we employ supervised fine-tuning to equip the model with dual thinking modes: fast thinking (trajectory-only) and slow thinking (enhanced with chain-of-thought reasoning). To further enhance planning performance and efficiency, we introduce a reinforcement fine-tuning method based on Group Relative Policy Optimization (GRPO), reducing unnecessary reasoning in straightforward scenarios. Extensive experiments across real-world and simulated datasets and benchmarks, including nuPlan, nuScenes, Waymo, and CARLA, demonstrate the competitive performance of AutoVLA in both open-loop and closed-loop settings. Qualitative results showcase the adaptive reasoning and accurate planning capabilities of AutoVLA in diverse scenarios.

While large reasoning models demonstrate strong performance on complex tasks, they lack the ability to adjust reasoning token usage based on task difficulty. This often leads to the "overthinking" problem -- excessive and unnecessary reasoning -- which, although potentially mitigated by human intervention to control the token budget, still fundamentally contradicts the goal of achieving fully autonomous AI. In this work, we propose Adaptive Reasoning Model (ARM), a reasoning model capable of adaptively selecting appropriate reasoning formats based on the task at hand. These formats include three efficient ones -- Direct Answer, Short CoT, and Code -- as well as a more elaborate format, Long CoT. To train ARM, we introduce Ada-GRPO, an adaptation of Group Relative Policy Optimization (GRPO), which addresses the format collapse issue in traditional GRPO. Ada-GRPO enables ARM to achieve high token efficiency, reducing tokens by an average of 30%, and up to 70%, while maintaining performance comparable to the model that relies solely on Long CoT. Furthermore, not only does it improve inference efficiency through reduced token generation, but it also brings a 2x speedup in training. In addition to the default Adaptive Mode, ARM supports two additional reasoning modes: 1) Instruction-Guided Mode, which allows users to explicitly specify the reasoning format via special tokens -- ideal when the appropriate format is known for a batch of tasks. 2) Consensus-Guided Mode, which aggregates the outputs of the three efficient formats and resorts to Long CoT in case of disagreement, prioritizing performance with higher token usage.

Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for improving large language models (LLMs) on reasoning tasks, with Group Relative Policy Optimization (GRPO) widely used in practice. Yet GRPO wastes substantial compute on negative groups: groups in which no sampled response is correct yield zero advantage and thus no gradient. We ask whether negative groups can be leveraged without extra supervision. Starting from a maximum-likelihood (MLE) objective in reward modeling, we show that the MLE gradient is equivalent to a policy gradient for a modified value function. This value function adds a confidence-weighted penalty on incorrect responses, imposing larger penalties on more confident mistakes. We refer to this as Likelihood Estimation with Negative Samples (LENS). LENS modifies GRPO to assign non-zero, confidence-dependent rewards to incorrect generations, making negative groups informative and converting previously wasted samples into useful gradient updates. On the MATH benchmark with Llama-3.1-8B and Qwen-2.5-3B, the proposed variant consistently outperforms GRPO baseline, with significant gains on harder items. These results demonstrate a principled and practical way to "rescue" negative groups, improving efficiency and performance in RLVR.

Time-series reasoning remains a significant challenge in multimodal large language models (MLLMs) due to the dynamic temporal patterns, ambiguous semantics, and lack of temporal priors. In this work, we introduce TimeMaster, a reinforcement learning (RL)-based method that enables time-series MLLMs to perform structured, interpretable reasoning directly over visualized time-series inputs and task prompts. TimeMaster adopts a three-part structured output format, reasoning, classification, and domain-specific extension, and is optimized via a composite reward function that aligns format adherence, prediction accuracy, and open-ended insight quality. The model is trained using a two-stage pipeline: we first apply supervised fine-tuning (SFT) to establish a good initialization, followed by Group Relative Policy Optimization (GRPO) at the token level to enable stable and targeted reward-driven improvement in time-series reasoning. We evaluate TimeMaster on the TimerBed benchmark across six real-world classification tasks based on Qwen2.5-VL-3B-Instruct. TimeMaster achieves state-of-the-art performance, outperforming both classical time-series models and few-shot GPT-4o by over 14.6% and 7.3% performance gain, respectively. Notably, TimeMaster goes beyond time-series classification: it also exhibits expert-like reasoning behavior, generates context-aware explanations, and delivers domain-aligned insights. Our results highlight that reward-driven RL can be a scalable and promising path toward integrating temporal understanding into time-series MLLMs.

Existing table understanding methods face challenges due to complex table structures and intricate logical reasoning. While supervised finetuning (SFT) dominates existing research, reinforcement learning (RL), such as Group Relative Policy Optimization (GRPO), has shown promise but struggled with low initial policy accuracy and coarse rewards in tabular contexts. In this paper, we introduce Table-R1, a three-stage RL framework that enhances multimodal table understanding through: (1) Warm-up that prompts initial perception and reasoning capabilities, (2) Perception Alignment GRPO (PA-GRPO), which employs continuous Tree-Edit-Distance Similarity (TEDS) rewards for recognizing table structures and contents, and (3) Hint-Completion GRPO (HC-GRPO), which utilizes fine-grained rewards of residual steps based on the hint-guided question. Extensive experiments demonstrate that Table-R1 can boost the model's table reasoning performance obviously on both held-in and held-out datasets, outperforming SFT and GRPO largely. Notably, Qwen2-VL-7B with Table-R1 surpasses larger specific table understanding models (e.g., Table-LLaVA 13B), even achieving comparable performance to the closed-source model GPT-4o on held-in datasets, demonstrating the efficacy of each stage of Table-R1 in overcoming initialization bottlenecks and reward sparsity, thereby advancing robust multimodal table understanding.

Visual reasoning abilities play a crucial role in understanding complex multimodal data, advancing both domain-specific applications and artificial general intelligence (AGI). Existing methods improve VLM reasoning via Chain-of-Thought (CoT) supervised fine-tuning, using meticulously annotated training data to enhance visual reasoning capabilities. However, this training paradigm may lead to overfitting and cognitive rigidity, restricting the model's ability to transfer visual reasoning skills across domains and limiting its real-world applicability. To address these limitations, we propose Reason-RFT, a novel reinforcement fine-tuning framework that significantly enhances generalization capabilities in visual reasoning tasks. Reason-RFT introduces a two-phase training framework for visual reasoning: (1) Supervised Fine-Tuning (SFT) with curated Chain-of-Thought (CoT) data activates the reasoning potential of Vision-Language Models (VLMs), followed by (2) Group Relative Policy Optimization (GRPO)-based reinforcement learning that generates multiple reasoning-response pairs, significantly enhancing generalization in visual reasoning tasks. To evaluate Reason-RFT's visual reasoning capabilities, we reconstructed a comprehensive dataset spanning visual counting, structure perception, and spatial transformation. Experimental results demonstrate Reasoning-RFT's three key advantages: (1) Performance Enhancement: achieving state-of-the-art results across multiple tasks, outperforming most mainstream open-source and proprietary models; (2) Generalization Superiority: consistently maintaining robust performance across diverse tasks and domains, outperforming alternative training paradigms; (3) Data Efficiency: excelling in few-shot learning scenarios while surpassing full-dataset SFT baselines. Project website: https://tanhuajie.github.io/ReasonRFT

Recent advances in Multimodal Large Language Models (MLLMs) have significantly improved 2D visual understanding, prompting interest in their application to complex 3D reasoning tasks. However, it remains unclear whether these models can effectively capture the detailed spatial information required for robust real-world performance, especially cross-view consistency, a key requirement for accurate 3D reasoning. Considering this issue, we introduce Viewpoint Learning, a task designed to evaluate and improve the spatial reasoning capabilities of MLLMs. We present the Viewpoint-100K dataset, consisting of 100K object-centric image pairs with diverse viewpoints and corresponding question-answer pairs. Our approach employs a two-stage fine-tuning strategy: first, foundational knowledge is injected to the baseline MLLM via Supervised Fine-Tuning (SFT) on Viewpoint-100K, resulting in significant improvements across multiple tasks; second, generalization is enhanced through Reinforcement Learning using the Group Relative Policy Optimization (GRPO) algorithm on a broader set of questions. Additionally, we introduce a hybrid cold-start initialization method designed to simultaneously learn viewpoint representations and maintain coherent reasoning thinking. Experimental results show that our approach significantly activates the spatial reasoning ability of MLLM, improving performance on both in-domain and out-of-domain reasoning tasks. Our findings highlight the value of developing foundational spatial skills in MLLMs, supporting future progress in robotics, autonomous systems, and 3D scene understanding.

As Test-Time Scaling emerges as an active research focus in the large language model community, advanced post-training methods increasingly emphasize extending chain-of-thought (CoT) generation length, thereby enhancing reasoning capabilities to approach Deepseek R1-like reasoning models. However, recent studies reveal that reasoning models (even Qwen3) consistently exhibit excessive thought redundancy in CoT generation. This overthinking issue arises from the inherent limitations of conventional outcome-reward reinforcement learning, which systematically overlooks the regulation of intermediate reasoning processes. This paper introduces Serial-Group Decaying-Reward Policy Optimization (S-GRPO), a novel reinforcement learning paradigm that enables models to implicitly evaluate the sufficiency of intermediate reasoning steps, thereby facilitating early exit in CoT generation. Unlike GRPO, which samples multiple possible reasoning paths in parallel (parallel group), S-GRPO only samples one reasoning path and serially selects multiple temporal positions from the path to exit thinking and directly generate answers (serial group). For correct answers within a serial group, rewards gradually decrease based on the exit positions along the reasoning path from front to back. This design encourages the model to produce more accurate and concise thoughts, while also incentivizing early thinking termination when appropriate. Empirical evaluations demonstrate that S-GRPO is compatible with state-of-the-art reasoning models, including Qwen3 and Deepseek-distill. Across diverse benchmarks such as GSM8K, AIME 2024, AMC 2023, MATH-500, and GPQA Diamond, S-GRPO achieves a substantial reduction in sequence length (35.4% - 61.1%) while simultaneously improving accuracy (absolute 0.72% - 6.08%).

Large language models (LLMs) achieve remarkable performance in code generation tasks. However, a significant performance disparity persists between popular programming languages (e.g., Python, C++) and others. To address this capability gap, we leverage the code translation task to train LLMs, thereby facilitating the transfer of coding proficiency across diverse programming languages. Moreover, we introduce OORL for training, a novel reinforcement learning (RL) framework that integrates on-policy and off-policy strategies. Within OORL, on-policy RL is applied during code translation, guided by a rule-based reward signal derived from unit tests. Complementing this coarse-grained rule-based reward, we propose Group Equivalent Preference Optimization (GEPO), a novel preference optimization method. Specifically, GEPO trains the LLM using intermediate representations (IRs) groups. LLMs can be guided to discern IRs equivalent to the source code from inequivalent ones, while also utilizing signals about the mutual equivalence between IRs within the group. This process allows LLMs to capture nuanced aspects of code functionality. By employing OORL for training with code translation tasks, LLMs improve their recognition of code functionality and their understanding of the relationships between code implemented in different languages. Extensive experiments demonstrate that our OORL for LLMs training with code translation tasks achieves significant performance improvements on code benchmarks across multiple programming languages.

We revisit policy-gradient optimization for Large Language Models (LLMs) from a single-stream perspective. Prevailing group-based methods like GRPO reduce variance with on-the-fly baselines but suffer from critical flaws: frequent degenerate groups erase learning signals, and synchronization barriers hinder scalability. We introduce Single-stream Policy Optimization (SPO), which eliminates these issues by design. SPO replaces per-group baselines with a persistent, KL-adaptive value tracker and normalizes advantages globally across the batch, providing a stable, low-variance learning signal for every sample. Being group-free, SPO enables higher throughput and scales effectively in long-horizon or tool-integrated settings where generation times vary. Furthermore, the persistent value tracker naturally enables an adaptive curriculum via prioritized sampling. Experiments using Qwen3-8B show that SPO converges more smoothly and attains higher accuracy than GRPO, while eliminating computation wasted on degenerate groups. Ablation studies confirm that SPO's gains stem from its principled approach to baseline estimation and advantage normalization, offering a more robust and efficient path for LLM reasoning. Across five hard math benchmarks with Qwen3 8B, SPO improves the average maj@32 by +3.4 percentage points (pp) over GRPO, driven by substantial absolute point gains on challenging datasets, including +7.3 pp on BRUMO 25, +4.4 pp on AIME 25, +3.3 pp on HMMT 25, and achieves consistent relative gain in pass@k across the evaluated k values. SPO's success challenges the prevailing trend of adding incidental complexity to RL algorithms, highlighting a path where fundamental principles, not architectural workarounds, drive the next wave of progress in LLM reasoning.

Critic-free reinforcement learning methods, particularly group policies, have attracted considerable attention for their efficiency in complex tasks. However, these methods rely heavily on multiple sampling and comparisons within the policy to estimate advantage, which may cause the policy to fall into local optimum and increase computational cost. To address these issues, we propose PVPO, an efficient reinforcement learning method enhanced by an advantage reference anchor and data pre-sampling. Specifically, we use the reference model to rollout in advance and employ the calculated reward score as a reference anchor. Our approach effectively corrects the cumulative bias introduced by intra-group comparisons and significantly reduces reliance on the number of rollouts during training. Meanwhile, the reference model can assess sample difficulty during data pre-sampling, enabling effective selection of high-gain data to improve training efficiency. Moreover, PVPO is orthogonal to other advanced critic-free RL algorithms, making it compatible with and complementary to these methods. Experiments conducted on nine datasets across two domains demonstrate that PVPO achieves State-Of-The-Art (SOTA) performance. Our approach not only demonstrates robust generalization across multiple tasks, but also exhibits scalable performance across models of varying scales.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

Social network simulation is developed to provide a comprehensive understanding of social networks in the real world, which can be leveraged for a wide range of applications such as group behavior emergence, policy optimization, and business strategy development. However, billions of individuals and their evolving interactions involved in social networks pose challenges in accurately reflecting real-world complexities. In this study, we propose a comprehensive Social Network Simulation System (GA-S3) that leverages newly designed Group Agents to make intelligent decisions regarding various online events. Unlike other intelligent agents that represent an individual entity, our group agents model a collection of individuals exhibiting similar behaviors, facilitating the simulation of large-scale network phenomena with complex interactions at a manageable computational cost. Additionally, we have constructed a social network benchmark from 2024 popular online events that contains fine-grained information on Internet traffic variations. The experiment demonstrates that our approach is capable of achieving accurate and highly realistic prediction results. Code is open at https://github.com/AI4SS/GAS-3.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they face significant challenges in embodied task planning scenarios that require continuous environmental understanding and action generation. Existing approaches generate open-loop action scripts based on static knowledge, making it difficult to learn causal relationships between actions and environmental feedback, particularly in partially observable environments. We introduce Embodied Planner-R1, a novel outcome-driven reinforcement learning framework that enables LLMs to develop interactive capabilities through autonomous exploration with minimal supervision. Our framework incorporates three key innovations: (1) Without human annotations, we employ pure reinforcement learning with group rollout, incorporating in-environment interaction through parallel exploration; (2) completion-driven sparse reward; and (3) Interactive Policy Optimization (IPO) for efficient learning from grouped trajectories. Across two challenging text-based Embodied planning benchmarks, Embodied Planner-R1 achieves impressive completion rates of 97.78% on ALFWorld and 79.92% on ScienceWorld, surpassing prior methods by a large margin, and suffers only a -3.66% drop in previously unseen environments, evidencing strong generalization.

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools, such as search engines and code interpreters, to solve tasks beyond the capabilities of language-only reasoning. While reinforcement learning (RL) has shown promise in improving TIR by optimizing final answer correctness, existing approaches often overlook the efficiency and cost associated with tool usage. This can lead to suboptimal behavior, including excessive tool calls that increase computational and financial overhead, or insufficient tool use that compromises answer quality. In this work, we propose Optimal Tool Call-controlled Policy Optimization (OTC-PO), a simple yet effective RL-based framework that encourages models to produce accurate answers with minimal tool calls. Our method introduces a tool-integrated reward that jointly considers correctness and tool efficiency, promoting high tool productivity. We instantiate this framework within both Proximal Policy Optimization (PPO) and Group Relative Preference Optimization (GRPO), resulting in OTC-PPO and OTC-GRPO. Experiments with Qwen-2.5 and Qwen-Math across multiple QA benchmarks show that our approach reduces tool calls by up to 73.1\% and improves tool productivity by up to 229.4\%, while maintaining comparable answer accuracy. To the best of our knowledge, this is the first RL-based framework that explicitly optimizes tool-use efficiency in TIR.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a "one-size-fits-all" approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

While reinforcement learning methods such as Group Relative Preference Optimization (GRPO) have significantly enhanced Large Language Models, adapting them to diffusion models remains challenging. In particular, GRPO demands a stochastic policy, yet the most cost-effective diffusion samplers are based on deterministic ODEs. Recent work addresses this issue by using inefficient SDE-based samplers to induce stochasticity, but this reliance on model-agnostic Gaussian noise leads to slow convergence. To resolve this conflict, we propose Direct Group Preference Optimization (DGPO), a new online RL algorithm that dispenses with the policy-gradient framework entirely. DGPO learns directly from group-level preferences, which utilize relative information of samples within groups. This design eliminates the need for inefficient stochastic policies, unlocking the use of efficient deterministic ODE samplers and faster training. Extensive results show that DGPO trains around 20 times faster than existing state-of-the-art methods and achieves superior performance on both in-domain and out-of-domain reward metrics. Code is available at https://github.com/Luo-Yihong/DGPO.

Diffusion-based text-to-speech (TTS) systems have made remarkable progress in zero-shot speech synthesis, yet optimizing all components for perceptual metrics remains challenging. Prior work with DMOSpeech demonstrated direct metric optimization for speech generation components, but duration prediction remained unoptimized. This paper presents DMOSpeech 2, which extends metric optimization to the duration predictor through a reinforcement learning approach. The proposed system implements a novel duration policy framework using group relative preference optimization (GRPO) with speaker similarity and word error rate as reward signals. By optimizing this previously unoptimized component, DMOSpeech 2 creates a more complete metric-optimized synthesis pipeline. Additionally, this paper introduces teacher-guided sampling, a hybrid approach leveraging a teacher model for initial denoising steps before transitioning to the student model, significantly improving output diversity while maintaining efficiency. Comprehensive evaluations demonstrate superior performance across all metrics compared to previous systems, while reducing sampling steps by half without quality degradation. These advances represent a significant step toward speech synthesis systems with metric optimization across multiple components. The audio samples, code and pre-trained models are available at https://dmospeech2.github.io/.

Multi-preference optimization enriches language-model alignment beyond pairwise preferences by contrasting entire sets of helpful and undesired responses, thereby enabling richer training signals for large language models. During self-play alignment, these models often produce numerous candidate answers per query, rendering it computationally infeasible to include all responses in the training objective. In this work, we propose Active Multi-Preference Optimization (AMPO), a novel approach that combines on-policy generation, a multi-preference group-contrastive loss, and active subset selection. Specifically, we score and embed large candidate pools of responses and then select a small, yet informative, subset that covers reward extremes and distinct semantic clusters for preference optimization. Our contrastive training scheme is capable of identifying not only the best and worst answers but also subtle, underexplored modes that are crucial for robust alignment. Theoretically, we provide guarantees for expected reward maximization using our active selection method, and empirically, AMPO achieves state-of-the-art results on AlpacaEval using Llama 8B.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Group Relative Policy Optimization (GRPO) enhances policy learning by computing gradients from relative comparisons among candidate outputs that share a common input prefix. Despite its effectiveness, GRPO introduces substantial computational overhead when processing long shared prefixes, which must be redundantly encoded for each group member. This inefficiency becomes a major scalability bottleneck in long-context learning scenarios. We propose Prefix Grouper, an efficient GRPO training algorithm that eliminates redundant prefix computation via a Shared-Prefix Forward strategy. In particular, by restructuring self-attention into two parts, our method enables the shared prefix to be encoded only once, while preserving full differentiability and compatibility with end-to-end training. We provide both theoretical and empirical evidence that Prefix Grouper is training-equivalent to standard GRPO: it yields identical forward outputs and backward gradients, ensuring that the optimization dynamics and final policy performance remain unchanged. Empirically, our experiments confirm that Prefix Grouper achieves consistent results while significantly reducing the computational cost of training, particularly in long-prefix scenarios. The proposed method is fully plug-and-play: it is compatible with existing GRPO-based architectures and can be seamlessly integrated into current training pipelines as a drop-in replacement, requiring no structural modifications and only minimal changes to input construction and attention computation. Prefix Grouper enables the use of larger group sizes under the same computational budget, thereby improving the scalability of GRPO to more complex tasks and larger models. Code is now available at https://github.com/johncaged/PrefixGrouper

Group Relative Policy Optimization (GRPO) is a prominent reinforcement learning algorithm for post-training Large Language Models (LLMs). It is commonly believed that GRPO necessitates a large group size to ensure stable training via precise statistical estimation, which incurs substantial computational overhead. In this work, we challenge this assumption by reframing GRPO as a form of contrastive learning, which reveals a fundamental connection to Direct Preference Optimization (DPO). Motivated by DPO's empirical success, we investigate the minimal two-rollout case (2-GRPO), a configuration previously deemed infeasible. We provide a rigorous theoretical analysis to validate 2-GRPO and demonstrate empirically that it achieves performance on par with 16-GRPO, despite using only 1/8 of the rollouts and reducing training time by over 70%.

Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer from the problem of sparse supervision. To address the challenge, we propose Tree-based Group Relative Policy Optimization (Tree-GRPO), a grouped agent RL method based on tree search, where each tree node represents the complete agent interaction step. By sharing common prefixes, the tree search sampling increases the number of rollouts achievable within a fixed budget of tokens or tool calls. Moreover, we find that the tree-structured trajectory naturally allows the construction of step-wise process supervised signals even using only the outcome reward. Based on this, Tree-GRPO estimates the grouped relative advantages both on intra-tree and inter-tree levels. Through theoretical analysis, we demonstrate that the objective of intra-tree level group relative policy optimization is equivalent to that of step-level direct preference learning. Experiments across 11 datasets and 3 types of QA tasks demonstrate the superiority of the proposed tree-based RL over the chain-based RL method.

Recent advances in reinforcement learning (RL) have significantly enhanced the reasoning capabilities of large language models (LLMs). Group Relative Policy Optimization (GRPO), a lightweight variant of Proximal Policy Optimization (PPO), improves efficiency but suffers from limited exploration and training instability, limiting its effectiveness on complex reasoning tasks. To address these challenges, we introduce EFRame, an Exploration-Filter-Replay framework that augments GRPO across three dimensions: additional rollouts enable deeper and more targeted exploration, online filtering removes low-quality samples to stabilize gradients and accelerate training, and experience replay amplifies rare yet informative trajectories for stable convergence. This unified framework establishes a principled training cycle that balances exploration, efficiency, and stability. Experiments on diverse reasoning benchmarks demonstrate that EFRame achieves consistent gains, including a 37.9\% relative improvement on Geometry3K over GRPO. EFRame further supports fine-grained sample categorization and precise entropy control, highlighting it as a robust solution for advancing deeper reasoning in LLMs. Our code is available at https://github.com/597358816/EFRame.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

Group Relative Policy Optimization (GRPO) has proven to be an effective tool for post-training language models (LMs). However, AI systems are increasingly expressed as modular programs that mix together multiple LM calls with distinct prompt templates and other tools, and it is not clear how best to leverage GRPO to improve these systems. We begin to address this challenge by defining mmGRPO, a simple multi-module generalization of GRPO that groups LM calls by module across rollouts and handles variable-length and interrupted trajectories. We find that mmGRPO, composed with automatic prompt optimization, improves accuracy by 11% on average across classification, many-hop search, and privacy-preserving delegation tasks against the post-trained LM, and by 5% against prompt optimization on its own. We open-source mmGRPO in DSPy as the dspy.GRPO optimizer.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

Reinforcement Learning (RL) has proven to be an effective post-training strategy for enhancing reasoning in vision-language models (VLMs). Group Relative Policy Optimization (GRPO) is a recent prominent method that encourages models to generate complete reasoning traces before answering, leading to increased token usage and computational cost. Inspired by the human-like thinking process-where people skip reasoning for easy questions but think carefully when needed-we explore how to enable VLMs to first decide when reasoning is necessary. To realize this, we propose TON, a two-stage training strategy: (i) a supervised fine-tuning (SFT) stage with a simple yet effective 'thought dropout' operation, where reasoning traces are randomly replaced with empty thoughts. This introduces a think-or-not format that serves as a cold start for selective reasoning; (ii) a GRPO stage that enables the model to freely explore when to think or not, while maximizing task-aware outcome rewards. Experimental results show that TON can reduce the completion length by up to 90% compared to vanilla GRPO, without sacrificing performance or even improving it. Further evaluations across diverse vision-language tasks-covering a range of reasoning difficulties under both 3B and 7B models-consistently reveal that the model progressively learns to bypass unnecessary reasoning steps as training advances. These findings shed light on the path toward human-like reasoning patterns in reinforcement learning approaches. Our code is available at https://github.com/kokolerk/TON.

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 41.5% length-controlled win rate on AlpacaEval 2.0 and a 38.3% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art iterative algorithm [Dong et al., 2024] under the BT model assumption. Additionally, our ablation study highlights the benefits of incorporating KL regularization for response length control.

Group-based reinforcement learning algorithms such as Group Reward Policy Optimization (GRPO) have proven effective for fine-tuning large language models (LLMs) with human feedback. However, generating and storing multiple responses per prompt incurs substantial memory overhead, especially as the sample group size increases, limiting scalability under constrained hardware. We propose Infinite Sampling, a framework that enables efficient and stable GRPO training by decoupling group size from GPU memory usage. It consists of: (1) micro sampling groups that decompose large groups into memory-feasible rounds; (2) continuous sampling that interleaves generation across groups to improve utilization; and (3) a length-aware scheduler combining token-conditioned sequence length prediction with a two-stage plan: global grouping via FPTAS and runtime refill via SJF. Experiments show that our Micro Sampling Groups reduce peak memory usage by over 50% compared to full-group decoding (e.g., from 21.55 GB to 10.64 GB on Qwen3-1.7B). Building on this, Infinite Sampling improves throughput by over 25% compared to the naive micro sampling group method, reducing decoding steps while maintaining full-length completions and memory usage. Our hybrid scheduling ensures efficient and stable GRPO training with larger groups under realistic GPU memory constraints.

Masked diffusion large language models (dLLMs) are emerging as promising alternatives to autoregressive LLMs, offering competitive performance while supporting unique generation capabilities such as inpainting. We explore how inpainting can inform RL algorithm design for dLLMs. Aligning LLMs with reinforcement learning faces an exploration challenge: sparse reward signals and sample waste when models fail to discover correct solutions. While this inefficiency affects LLMs broadly, dLLMs offer a distinctive opportunity--their inpainting ability can guide exploration. We introduce IGPO (Inpainting Guided Policy Optimization), an RL framework that strategically inserts partial ground-truth reasoning traces during online sampling. Unlike providing full solutions, inpainting steers exploration toward promising trajectory spaces while preserving self-generated reasoning, bridging supervised fine-tuning and reinforcement learning. We apply IGPO to group-based optimization methods such as GRPO, where exploration failures cause zero advantages and gradients. IGPO restores meaningful gradients while improving sample efficiency. We also propose supervised fine-tuning on synthetically rewritten concise traces that better align with dLLM generation patterns. With additional techniques including entropy-based filtering, our training recipe yields substantial gains across three mathematical benchmarks--GSM8K, Math500, and AMC--achieving new state-of-the-art results for full-attention masked dLLMs.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

Recent advances of reasoning models, exemplified by OpenAI's o1 and DeepSeek's R1, highlight the significant potential of Reinforcement Learning (RL) to enhance the reasoning capabilities of Large Language Models (LLMs). However, replicating these advancements across diverse domains remains challenging due to limited methodological transparency. In this work, we present two-Staged history-Resampling Policy Optimization (SRPO), which successfully surpasses the performance of DeepSeek-R1-Zero-32B on the AIME24 and LiveCodeBench benchmarks. SRPO achieves this using the same base model as DeepSeek (i.e. Qwen2.5-32B) and relies solely on RL, without prior Supervised Fine-Tuning (SFT). Building upon Group Relative Policy Optimization (GRPO), we introduce two key methodological innovations: (1) a two-stage cross-domain training paradigm designed to balance the development of mathematical reasoning and coding proficiency, and (2) History Resampling (HR), a technique to address ineffective samples. Our comprehensive experiments validate the effectiveness of our approach, dedicating to offer valuable insights into scaling LLM reasoning capabilities across diverse tasks.

Group Relative Policy Optimization (GRPO) has shown strong potential for flow-matching-based text-to-image (T2I) generation, but it faces two key limitations: inaccurate advantage attribution, and the neglect of temporal dynamics of generation. In this work, we argue that shifting the optimization paradigm from the step level to the chunk level can effectively alleviate these issues. Building on this idea, we propose Chunk-GRPO, the first chunk-level GRPO-based approach for T2I generation. The insight is to group consecutive steps into coherent 'chunk's that capture the intrinsic temporal dynamics of flow matching, and to optimize policies at the chunk level. In addition, we introduce an optional weighted sampling strategy to further enhance performance. Extensive experiments show that ChunkGRPO achieves superior results in both preference alignment and image quality, highlighting the promise of chunk-level optimization for GRPO-based methods.

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time.

This paper explores multi-scenario optimization on large platforms using multi-agent reinforcement learning (MARL). We address this by treating scenarios like search, recommendation, and advertising as a cooperative, partially observable multi-agent decision problem. We introduce the Multi-Agent Recurrent Deterministic Policy Gradient (MARDPG) algorithm, which aligns different scenarios under a shared objective and allows for strategy communication to boost overall performance. Our results show marked improvements in metrics such as click-through rate (CTR), conversion rate, and total sales, confirming our method's efficacy in practical settings.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

Reinforcement learning (RL)-based post-training has been crucial for enabling multi-step reasoning in large reasoning models (LRMs), yet current reward schemes are typically outcome-centric. We propose PM4GRPO, a reasoning-aware Group Relative Policy Optimization (GRPO) that augments standard answer/format rewards with signals over the reasoning procedure. To this end, process mining techniques are utilized to compute a scalar conformance reward that measures how closely a policy model's reasoning aligns with the pretrained teacher model. The empirical results on five benchmarks demonstrate that PM4GRPO significantly outperforms existing methodologies for GRPO-based post-training. These results highlight that leveraging process mining for reasoning-aware GRPO effectively enhances the reasoning capabilities of policy models.

The success of AI assistants based on language models (LLMs) hinges crucially on Reinforcement Learning from Human Feedback (RLHF), which enables the generation of responses more aligned with human preferences. As universal AI assistants, there's a growing expectation for them to perform consistently across various domains. However, previous work shows that Reinforcement Learning (RL) often exploits shortcuts to attain high rewards and overlooks challenging samples. This focus on quick reward gains undermines both the stability in training and the model's ability to generalize to new, unseen data. In this work, we propose a novel approach that can learn a consistent policy via RL across various data groups or domains. Given the challenges associated with acquiring group annotations, our method automatically classifies data into different groups, deliberately maximizing performance variance. Then, we optimize the policy to perform well on challenging groups. Lastly, leveraging the established groups, our approach adaptively adjusts the exploration space, allocating more learning capacity to more challenging data and preventing the model from over-optimizing on simpler data. Experimental results indicate that our approach significantly enhances training stability and model generalization.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

Recently, the impressive empirical success of policy gradient (PG) methods has catalyzed the development of their theoretical foundations. Despite the huge efforts directed at the design of efficient stochastic PG-type algorithms, the understanding of their convergence to a globally optimal policy is still limited. In this work, we develop improved global convergence guarantees for a general class of Fisher-non-degenerate parameterized policies which allows to address the case of continuous state action spaces. First, we propose a Normalized Policy Gradient method with Implicit Gradient Transport (N-PG-IGT) and derive a mathcal{O}(varepsilon^{-2.5}) sample complexity of this method for finding a global varepsilon-optimal policy. Improving over the previously known mathcal{O}(varepsilon^{-3}) complexity, this algorithm does not require the use of importance sampling or second-order information and samples only one trajectory per iteration. Second, we further improve this complexity to mathcal{mathcal{O} }(varepsilon^{-2}) by considering a Hessian-Aided Recursive Policy Gradient ((N)-HARPG) algorithm enhanced with a correction based on a Hessian-vector product. Interestingly, both algorithms are (i) simple and easy to implement: single-loop, do not require large batches of trajectories and sample at most two trajectories per iteration; (ii) computationally and memory efficient: they do not require expensive subroutines at each iteration and can be implemented with memory linear in the dimension of parameters.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

Developing AI agents that can robustly adapt to dramatically different strategic landscapes without retraining is a central challenge for multi-agent learning. Pok\'emon Video Game Championships (VGC) is a domain with an extraordinarily large space of possible team configurations of approximately 10^{139} - far larger than those of Dota or Starcraft. The highly discrete, combinatorial nature of team building in Pok\'emon VGC causes optimal strategies to shift dramatically depending on both the team being piloted and the opponent's team, making generalization uniquely challenging. To advance research on this problem, we introduce VGC-Bench: a benchmark that provides critical infrastructure, standardizes evaluation protocols, and supplies human-play datasets and a range of baselines - from large-language-model agents and behavior cloning to reinforcement learning and empirical game-theoretic methods such as self-play, fictitious play, and double oracle. In the restricted setting where an agent is trained and evaluated on a single-team configuration, our methods are able to win against a professional VGC competitor. We extensively evaluated all baseline methods over progressively larger team sets and find that even the best-performing algorithm in the single-team setting struggles at scaling up as team size grows. Thus, policy generalization across diverse team strategies remains an open challenge for the community. Our code is open sourced at https://github.com/cameronangliss/VGC-Bench.

We investigate the effectiveness of reinforcement learning methods for finetuning large language models when transitioning from offline to semi-online to fully online regimes for both verifiable and non-verifiable tasks. Our experiments cover training on verifiable math as well as non-verifiable instruction following with a set of benchmark evaluations for both. Across these settings, we extensively compare online and semi-online Direct Preference Optimization and Group Reward Policy Optimization objectives, and surprisingly find similar performance and convergence between these variants, which all strongly outperform offline methods. We provide a detailed analysis of the training dynamics and hyperparameter selection strategies to achieve optimal results. Finally, we show that multi-tasking with verifiable and non-verifiable rewards jointly yields improved performance across both task types.

Large Language Models (LLMs) as automatic evaluators, commonly referred to as LLM-as-a-Judge, have also attracted growing attention. This approach plays a vital role in aligning LLMs with human judgments, providing accurate and reliable assessments. However, LLM-based judgment models often exhibit judgment preference bias during the evaluation phase, tending to favor responses generated by themselves, undermining the reliability of their judgments. This paper introduces the Group-Based Polling Optimization (Genii), an unsupervised multi-agent collaborative optimization framework that mitigates the inherent judgment preference bias of judgment models. Specifically, Genii integrates various LLM-based judgment models into a multi-agent system and simulates the interactive client-server polling mechanism to optimize each client agent unsupervisedly. Our experiments demonstrate that Genii outperforms supervised models trained on annotated judgment data, while requiring no human-labeled annotations. Genii consistently improves performance across different client agents during the polling, even when weaker models act as server agents. Further analysis reveals that Genii effectively mitigates judgment preference bias of LLM-based judgment models, demonstrating its effectiveness. All codes are available at https://github.com/NEUIR/Genii.

Multimodal Large Language Models (MLLMs) have gained significant traction for their ability to process diverse input data types and generate coherent, contextually relevant outputs across various applications. While supervised fine-tuning (SFT) has been the predominant approach to enhance MLLM capabilities in task-specific optimization, it often falls short in fostering crucial generalized reasoning abilities. Although reinforcement learning (RL) holds great promise in overcoming these limitations, it encounters two significant challenges: (1) its generalized capacities in multimodal tasks remain largely unexplored, and (2) its training constraints, including the constant Kullback-Leibler divergence or the clamp strategy, often result in suboptimal bottlenecks. To address these challenges, we propose OThink-MR1, an advanced MLLM equipped with profound comprehension and reasoning capabilities across multimodal tasks. Specifically, we introduce Group Relative Policy Optimization with a dynamic Kullback-Leibler strategy (GRPO-D), which markedly enhances reinforcement learning (RL) performance. For Qwen2-VL-2B-Instruct, GRPO-D achieves a relative improvement of more than 5.72% over SFT and more than 13.59% over GRPO in same-task evaluation on two adapted datasets. Furthermore, GRPO-D demonstrates remarkable cross-task generalization capabilities, with an average relative improvement of more than 61.63% over SFT in cross-task evaluation. These results highlight that the MLLM trained with GRPO-D on one multimodal task can be effectively transferred to another task, underscoring the superior generalized reasoning capabilities of our proposed OThink-MR1 model.

The study of decentralized learning or independent learning in cooperative multi-agent reinforcement learning has a history of decades. Recently empirical studies show that independent PPO (IPPO) can obtain good performance, close to or even better than the methods of centralized training with decentralized execution, in several benchmarks. However, decentralized actor-critic with convergence guarantee is still open. In this paper, we propose decentralized policy optimization (DPO), a decentralized actor-critic algorithm with monotonic improvement and convergence guarantee. We derive a novel decentralized surrogate for policy optimization such that the monotonic improvement of joint policy can be guaranteed by each agent independently optimizing the surrogate. In practice, this decentralized surrogate can be realized by two adaptive coefficients for policy optimization at each agent. Empirically, we compare DPO with IPPO in a variety of cooperative multi-agent tasks, covering discrete and continuous action spaces, and fully and partially observable environments. The results show DPO outperforms IPPO in most tasks, which can be the evidence for our theoretical results.

A large amount of work has been done in Multi-Agent Systems (MAS) for modeling and solving problems with multiple interacting agents. However, most LLMs are pretrained independently and not specifically optimized for coordination. Existing LLM fine-tuning frameworks rely on individual rewards, which require complex reward designs for each agent to encourage collaboration. To address these challenges, we model LLM collaboration as a cooperative Multi-Agent Reinforcement Learning (MARL) problem. We develop a multi-agent, multi-turn algorithm, Multi-Agent Group Relative Policy Optimization (MAGRPO), to solve it, building on current RL approaches for LLMs as well as MARL techniques. Our experiments on LLM writing and coding collaboration demonstrate that fine-tuning MAS with MAGRPO enables agents to generate high-quality responses efficiently through effective cooperation. Our approach opens the door to using other MARL methods for LLMs and highlights the associated challenges.

We introduce VisTA, a new reinforcement learning framework that empowers visual agents to dynamically explore, select, and combine tools from a diverse library based on empirical performance. Existing methods for tool-augmented reasoning either rely on training-free prompting or large-scale fine-tuning; both lack active tool exploration and typically assume limited tool diversity, and fine-tuning methods additionally demand extensive human supervision. In contrast, VisTA leverages end-to-end reinforcement learning to iteratively refine sophisticated, query-specific tool selection strategies, using task outcomes as feedback signals. Through Group Relative Policy Optimization (GRPO), our framework enables an agent to autonomously discover effective tool-selection pathways without requiring explicit reasoning supervision. Experiments on the ChartQA, Geometry3K, and BlindTest benchmarks demonstrate that VisTA achieves substantial performance gains over training-free baselines, especially on out-of-distribution examples. These results highlight VisTA's ability to enhance generalization, adaptively utilize diverse tools, and pave the way for flexible, experience-driven visual reasoning systems.

We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multi-agent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies for each agent that leads to more robust multi-agent policies. We show the strength of our approach compared to existing methods in cooperative as well as competitive scenarios, where agent populations are able to discover various physical and informational coordination strategies.

Large Language Model (LLM)-driven Multi-agent systems (Mas) have recently emerged as a powerful paradigm for tackling complex real-world tasks. However, existing Mas construction methods typically rely on manually crafted interaction mechanisms or heuristic rules, introducing human biases and constraining the autonomous ability. Even with recent advances in adaptive Mas construction, existing systems largely remain within the paradigm of semi-autonomous patterns. In this work, we propose MasHost, a Reinforcement Learning (RL)-based framework for autonomous and query-adaptive Mas design. By formulating Mas construction as a graph search problem, our proposed MasHost jointly samples agent roles and their interactions through a unified probabilistic sampling mechanism. Beyond the accuracy and efficiency objectives pursued in prior works, we introduce component rationality as an additional and novel design principle in Mas. To achieve this multi-objective optimization, we propose Hierarchical Relative Policy Optimization (HRPO), a novel RL strategy that collaboratively integrates group-relative advantages and action-wise rewards. To our knowledge, our proposed MasHost is the first RL-driven framework for autonomous Mas graph construction. Extensive experiments on six benchmarks demonstrate that MasHost consistently outperforms most competitive baselines, validating its effectiveness, efficiency, and structure rationality.

Direct Preference Optimization (DPO) has become a popular approach for aligning language models using pairwise preferences. However, in practical post-training pipelines, on-policy generation typically yields multiple candidate responses per prompt, which are scored by a reward model to guide learning. In this setting, we propose Multi-Preference Optimization (MPO), a generalization of DPO that optimizes over entire sets of responses by extending the Bradley-Terry model to groupwise comparisons between chosen and rejected sets. To further enhance learning, MPO employs deviation-based weighting, which emphasizes outlier responses that deviate most from the mean reward, effectively inducing a self-paced curriculum. We theoretically prove that MPO reduces alignment bias at a rate of Oleft(1{n}right) with respect to the number of responses per query. Empirically, MPO achieves state-of-the-art performance on the UltraFeedback benchmark and yields up to sim 17.5% improvement over the state-of-the-art baseline in length-controlled win rate on AlpacaEval2, establishing a new baseline for preference-based alignment

As test-time scaling becomes a pivotal research frontier in Large Language Models (LLMs) development, contemporary and advanced post-training methodologies increasingly focus on extending the generation length of long Chain-of-Thought (CoT) responses to enhance reasoning capabilities toward DeepSeek R1-like performance. However, recent studies reveal a persistent overthinking phenomenon in state-of-the-art reasoning models, manifesting as excessive redundancy or repetitive thinking patterns in long CoT responses. To address this issue, in this paper, we propose a simple yet effective two-stage reinforcement learning framework for achieving concise reasoning in LLMs, named ConciseR. Specifically, the first stage, using more training steps, aims to incentivize the model's reasoning capabilities via Group Relative Policy Optimization with clip-higher and dynamic sampling components (GRPO++), and the second stage, using fewer training steps, explicitly enforces conciseness and improves efficiency via Length-aware Group Relative Policy Optimization (L-GRPO). Significantly, ConciseR only optimizes response length once all rollouts of a sample are correct, following the "walk before you run" principle. Extensive experimental results demonstrate that our ConciseR model, which generates more concise CoT reasoning responses, outperforms recent state-of-the-art reasoning models with zero RL paradigm across AIME 2024, MATH-500, AMC 2023, Minerva, and Olympiad benchmarks.

This paper develops a policy learning method for tuning a pre-trained policy to adapt to additional tasks without altering the original task. A method named Adaptive Policy Gradient (APG) is proposed in this paper, which combines Bellman's principle of optimality with the policy gradient approach to improve the convergence rate. This paper provides theoretical analysis which guarantees the convergence rate and sample complexity of O(1/T) and O(1/epsilon), respectively, where T denotes the number of iterations and epsilon denotes the accuracy of the resulting stationary policy. Furthermore, several challenging numerical simulations, including cartpole, lunar lander, and robot arm, are provided to show that APG obtains similar performance compared to existing deterministic policy gradient methods while utilizing much less data and converging at a faster rate.

Recently, Large Language Models (LLMs) have rapidly evolved, approaching Artificial General Intelligence (AGI) while benefiting from large-scale reinforcement learning to enhance Human Alignment (HA) and Reasoning. Recent reward-based optimization algorithms, such as Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO) have achieved significant performance on reasoning tasks, whereas preference-based optimization algorithms such as Direct Preference Optimization (DPO) significantly improve the performance of LLMs on human alignment. However, despite the strong performance of reward-based optimization methods in alignment tasks , they remain vulnerable to reward hacking. Furthermore, preference-based algorithms (such as Online DPO) haven't yet matched the performance of reward-based optimization algorithms (like PPO) on reasoning tasks, making their exploration in this specific area still a worthwhile pursuit. Motivated by these challenges, we propose the Trust Region Preference Approximation (TRPA) algorithm, which integrates rule-based optimization with preference-based optimization for reasoning tasks. As a preference-based algorithm, TRPA naturally eliminates the reward hacking issue. TRPA constructs preference levels using predefined rules, forms corresponding preference pairs, and leverages a novel optimization algorithm for RL training with a theoretical monotonic improvement guarantee. Experimental results demonstrate that TRPA not only achieves competitive performance on reasoning tasks but also exhibits robust stability. The code of this paper are released and updating on https://github.com/XueruiSu/Trust-Region-Preference-Approximation.git.

Recent studies, including DeepSeek-R1 and Kimi-k1.5, have demonstrated that reinforcement learning with rule-based, binary-valued reward functions can significantly enhance the reasoning capabilities of large language models. These models primarily utilize REINFORCE-based policy optimization techniques, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation remains: current policy optimization methods either neglect reward normalization or employ static normalization strategies, which fail to adapt to the dynamic nature of policy updates during training. This may result in unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel policy optimization method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. BNPO aligns the normalization with the changing policy distribution, enabling more precise and lower-variance gradient estimation, which in turn promotes stable training dynamics. We provide theoretical analysis demonstrating BNPO's variance-reducing properties and show that it generalizes both REINFORCE and GRPO under binary-valued reward settings. Furthermore, we introduce an advantage decomposition mechanism to extend BNPO's applicability to more complex reward systems. Experimental results confirm that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks. The code is available at https://github.com/changyi7231/BNPO.

Policy optimization methods with function approximation are widely used in multi-agent reinforcement learning. However, it remains elusive how to design such algorithms with statistical guarantees. Leveraging a multi-agent performance difference lemma that characterizes the landscape of multi-agent policy optimization, we find that the localized action value function serves as an ideal descent direction for each local policy. Motivated by the observation, we present a multi-agent PPO algorithm in which the local policy of each agent is updated similarly to vanilla PPO. We prove that with standard regularity conditions on the Markov game and problem-dependent quantities, our algorithm converges to the globally optimal policy at a sublinear rate. We extend our algorithm to the off-policy setting and introduce pessimism to policy evaluation, which aligns with experiments. To our knowledge, this is the first provably convergent multi-agent PPO algorithm in cooperative Markov games.

Reinforcement Learning has emerged as a post-training approach to elicit agentic RAG behaviors such as search and planning from language models. However, compact language models (e.g., 0.5B parameters) struggle due to poor reasoning ability, resulting in sparse rewards and unstable training. To overcome these difficulties, we propose Distillation-Guided Policy Optimization (DGPO), which addresses the challenges through cold-start initialization from teacher demonstrations and continuous teacher guidance during policy optimization. To systematically evaluate our approach, we introduce Agentic RAG Capabilities (ARC), a fine-grained metric analyzing reasoning, search coordination, and response synthesis. Comprehensive experiments demonstrate that DGPO enables compact models to achieve sophisticated agentic search behaviors, even outperforming the larger teacher model in some cases. DGPO makes agentic RAG feasible in computing resource-constrained environments.

Reinforcement Learning (RL) has been used to finetune Large Language Models (LLMs) using a reward model trained from preference data, to better align with human judgment. The recently introduced direct alignment methods, which are often simpler, more stable, and computationally lighter, can more directly achieve this. However, these approaches cannot optimize arbitrary rewards, and the preference-based ones are not the only rewards of interest for LLMs (eg., unit tests for code generation or textual entailment for summarization, among others). RL-finetuning is usually done with a variation of policy gradient, which calls for on-policy or near-on-policy samples, requiring costly generations. We introduce Contrastive Policy Gradient, or CoPG, a simple and mathematically principled new RL algorithm that can estimate the optimal policy even from off-policy data. It can be seen as an off-policy policy gradient approach that does not rely on important sampling techniques and highlights the importance of using (the right) state baseline. We show this approach to generalize the direct alignment method IPO (identity preference optimization) and classic policy gradient. We experiment with the proposed CoPG on a toy bandit problem to illustrate its properties, as well as for finetuning LLMs on a summarization task, using a learned reward function considered as ground truth for the purpose of the experiments.

Multi-agent systems (MAS) and reinforcement learning (RL) are widely used to enhance the agentic capabilities of large language models (LLMs). MAS improves task performance through role-based orchestration, while RL uses environmental rewards to learn stronger policies, such as GRPO-style optimization. However, applying on-policy RL to MAS remains underexplored and presents unique challenges. Algorithmically, standard GRPO grouping assumptions break down because prompts vary by role and by turn. System-wise, the training stack must support MAS-workflow rollouts and on-policy updates for both single-policy and multi-policy models. We propose AT-GRPO, which includes (i) an agent- and turn-wise grouped RL algorithm tailored to MAS and (ii) a training system that supports both single- and multi-policy regimes. Across game, planning, coding, and math tasks, AT-GRPO delivers substantial gains. On long-horizon planning, it increases accuracy from a 14.0 to 47.0 percent single-agent RL baseline to 96.0 to 99.5 percent. It also improves reasoning performance, with average gains of 3.87 to 7.62 percent on coding tasks and 9.0 to 17.93 percent on math. Code and environments are available at: https://github.com/pettingllms-ai/PettingLLMs.

With the proliferation of red-teaming strategies for Large Language Models (LLMs), the deficiency in the literature about improving the safety and robustness of LLM defense strategies is becoming increasingly pronounced. This paper introduces the LLM-based sentinel model as a plug-and-play prefix module designed to reconstruct the input prompt with just a few (<30) additional tokens, effectively reducing toxicity in responses from target LLMs. The sentinel model naturally overcomes the parameter inefficiency and limited model accessibility for fine-tuning large target models. We employ an interleaved training regimen using Proximal Policy Optimization (PPO) to optimize both red team and sentinel models dynamically, incorporating a value head-sharing mechanism inspired by the multi-agent centralized critic to manage the complex interplay between agents. Our extensive experiments across text-to-text and text-to-image demonstrate the effectiveness of our approach in mitigating toxic outputs, even when dealing with larger models like Llama-2, GPT-3.5 and Stable-Diffusion, highlighting the potential of our framework in enhancing safety and robustness in various applications.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

In recent years, various powerful policy gradient algorithms have been proposed in deep reinforcement learning. While all these algorithms build on the Policy Gradient Theorem, the specific design choices differ significantly across algorithms. We provide a holistic overview of on-policy policy gradient algorithms to facilitate the understanding of both their theoretical foundations and their practical implementations. In this overview, we include a detailed proof of the continuous version of the Policy Gradient Theorem, convergence results and a comprehensive discussion of practical algorithms. We compare the most prominent algorithms on continuous control environments and provide insights on the benefits of regularization. All code is available at https://github.com/Matt00n/PolicyGradientsJax.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

Curriculum learning plays a crucial role in enhancing the training efficiency of large language models (LLMs) on reasoning tasks. However, existing methods often fail to adequately account for variations in prompt difficulty or rely on simplistic filtering mechanisms to select prompt datasets within a narrow criterion range, resulting in significant computational waste. In this work, we approach the problem from the perspective of reinforcement learning gradient optimization, offering a systematic and theoretical investigation into how to improve the training efficiency of LLMs. We identify two key factors influencing training efficiency: the selection of training prompts and the allocation of rollout quantities across different prompts. Our theoretical analysis reveals that the sampling distribution of prompts dictates the convergence rate of gradient descent, while the allocation of the rollout quantity influences the consistency and stability of overall gradient updates. Based on these insights, we propose CurES, an efficient training method that accelerates convergence and employs Bayesian posterior estimation to minimize computational overhead. Experiments demonstrate that our CurES outperforms Group Relative Policy Optimization (GRPO) by +3.30 points and +4.82 points with 1.5B and 7B models, respectively. Additionally, CurES exhibits faster convergence compared to baselines, including GRPO.

In problem-solving, we humans can come up with multiple novel solutions to the same problem. However, reinforcement learning algorithms can only produce a set of monotonous policies that maximize the cumulative reward but lack diversity and novelty. In this work, we address the problem of generating novel policies in reinforcement learning tasks. Instead of following the multi-objective framework used in existing methods, we propose to rethink the problem under a novel perspective of constrained optimization. We first introduce a new metric to evaluate the difference between policies and then design two practical novel policy generation methods following the new perspective. The two proposed methods, namely the Constrained Task Novel Bisector (CTNB) and the Interior Policy Differentiation (IPD), are derived from the feasible direction method and the interior point method commonly known in the constrained optimization literature. Experimental comparisons on the MuJoCo control suite show our methods can achieve substantial improvement over previous novelty-seeking methods in terms of both the novelty of policies and their performances in the primal task.

This research introduces a novel AI techniques as Mixture-of-Experts Transformers with Group Relative Policy Optimization (GRPO) for voice health care applications on voice pathology detection. With the architectural innovations, we adopt advanced training paradigms inspired by reinforcement learning, namely Proximal Policy Optimization (PPO) and Group-wise Regularized Policy Optimization (GRPO), to enhance model stability and performance. Experiments conducted on a synthetically generated voice pathology dataset demonstrate that our proposed models significantly improve diagnostic accuracy, F1 score, and ROC-AUC compared to conventional approaches. These findings underscore the potential of integrating transformer architectures with novel training strategies to advance automated voice pathology detection and ultimately contribute to more effective healthcare delivery. The code we used to train and evaluate our models is available at https://github.com/enkhtogtokh/voicegrpo

On-demand ride-sharing platforms face the fundamental challenge of dynamically bundling passengers with diverse origins and destinations and matching them with vehicles in real time, all under significant uncertainty. Recently, MARL has emerged as a promising solution for this problem, leveraging decentralized learning to address the curse of dimensionality caused by the large number of agents in the ride-hailing market and the resulting expansive state and action spaces. However, conventional MARL-based ride-sharing approaches heavily rely on the accurate estimation of Q-values or V-values, which becomes problematic in large-scale, highly uncertain environments. Specifically, most of these approaches adopt an independent paradigm, exacerbating this issue, as each agent treats others as part of the environment, leading to unstable training and substantial estimation bias in value functions. To address these challenges, we propose two novel alternative methods that bypass value function estimation. First, we adapt GRPO to ride-sharing, replacing the PPO baseline with the group average reward to eliminate critic estimation errors and reduce training bias. Second, inspired by GRPO's full utilization of group reward information, we customize the PPO framework for ride-sharing platforms and show that, under a homogeneous fleet, the optimal policy can be trained using only one-step rewards - a method we term One-Step Policy Optimization (OSPO). Experiments on a real-world Manhattan ride-hailing dataset demonstrate that both GRPO and OSPO achieve superior performance across most scenarios, efficiently optimizing pickup times and the number of served orders using simple MLP networks.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

Discrete diffusion models have recently gained significant attention due to their ability to process complex discrete structures for language modeling. However, fine-tuning these models with policy gradient methods, as is commonly done in Reinforcement Learning from Human Feedback (RLHF), remains a challenging task. We propose an efficient, broadly applicable, and theoretically justified policy gradient algorithm, called Score Entropy Policy Optimization (SEPO), for fine-tuning discrete diffusion models over non-differentiable rewards. Our numerical experiments across several discrete generative tasks demonstrate the scalability and efficiency of our method. Our code is available at https://github.com/ozekri/SEPO.

This paper introduces Completion Pruning Policy Optimization (CPPO) to accelerate the training of reasoning models based on Group Relative Policy Optimization (GRPO). GRPO, while effective, incurs high training costs due to the need for sampling multiple completions for each question. Our experiment and theoretical analysis reveals that the number of completions impacts model accuracy yet increases training time multiplicatively, and not all completions contribute equally to policy training -- their contribution depends on their relative advantage. To address these issues, we propose CPPO, which prunes completions with low absolute advantages, significantly reducing the number needed for gradient calculation and updates. Additionally, we introduce a dynamic completion allocation strategy to maximize GPU utilization by incorporating additional questions, further enhancing training efficiency. Experimental results demonstrate that CPPO achieves up to 8.32times speedup on GSM8K and 3.51times on Math while preserving or even enhancing the accuracy compared to the original GRPO. We release our code at https://github.com/lzhxmu/CPPO.

This paper introduces TempSamp-R1, a new reinforcement fine-tuning framework designed to improve the effectiveness of adapting multimodal large language models (MLLMs) to video temporal grounding tasks. We reveal that existing reinforcement learning methods, such as Group Relative Policy Optimization (GRPO), rely on on-policy sampling for policy updates. However, in tasks with large temporal search spaces, this strategy becomes both inefficient and limited in performance, as it often fails to identify temporally accurate solutions. To address this limitation, TempSamp-R1 leverages ground-truth annotations as off-policy supervision to provide temporally precise guidance, effectively compensating for the sparsity and misalignment in on-policy solutions. To further stabilize training and reduce variance in reward-based updates, TempSamp-R1 provides a non-linear soft advantage computation method that dynamically reshapes the reward feedback via an asymmetric transformation. By employing a hybrid Chain-of-Thought (CoT) training paradigm, TempSamp-R1 optimizes a single unified model to support both CoT and non-CoT inference modes, enabling efficient handling of queries with varying reasoning complexity. Experimental results demonstrate that TempSamp-R1 outperforms GRPO-based baselines, establishing new state-of-the-art performance on benchmark datasets: Charades-STA ([email protected]: 52.9%, +2.7%), ActivityNet Captions ([email protected]: 56.0%, +5.3%), and QVHighlights (mAP: 30.0%, +3.0%). Moreover, TempSamp-R1 shows robust few-shot generalization capabilities under limited data. Code: https://github.com/HVision-NKU/TempSamp-R1

We present Seg-R1, a preliminary exploration of using reinforcement learning (RL) to enhance the pixel-level understanding and reasoning capabilities of large multimodal models (LMMs). Starting with foreground segmentation tasks, specifically camouflaged object detection (COD) and salient object detection (SOD), our approach enables the LMM to generate point and bounding box prompts in the next-token fashion, which are then used to guide SAM2 in producing segmentation masks. We introduce Group Relative Policy Optimization (GRPO) into the segmentation domain, equipping the LMM with pixel-level comprehension through a carefully designed training strategy. Notably, Seg-R1 achieves remarkable performance with purely RL-based training, achieving .873 S-measure on COD10K without complex model modification. Moreover, we found that pure RL training demonstrates strong open-world generalization. Despite being trained solely on foreground segmentation image-mask pairs without text supervision, Seg-R1 achieves impressive zero-shot performance on referring segmentation and reasoning segmentation tasks, with 71.4 cIoU on RefCOCOg test and 56.7 gIoU on ReasonSeg test, outperforming models fully supervised on these datasets.

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios--including sample replay and partial rollout--BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.

We present a novel unified bilevel optimization-based framework, PARL, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named A-PARL to solve PARL problem, establishing sample complexity bounds of order O(1/T). Our empirical results substantiate that the proposed PARL can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.

Reinforcement learning from human feedback (RLHF) methods are emerging as a way to fine-tune diffusion models (DMs) for visual generation. However, commonly used on-policy strategies are limited by the generalization capability of the reward model, while off-policy approaches require large amounts of difficult-to-obtain paired human-annotated data, particularly in visual generation tasks. To address the limitations of both on- and off-policy RLHF, we propose a preference optimization method that aligns DMs with preferences without relying on reward models or paired human-annotated data. Specifically, we introduce a Semi-Policy Preference Optimization (SePPO) method. SePPO leverages previous checkpoints as reference models while using them to generate on-policy reference samples, which replace "losing images" in preference pairs. This approach allows us to optimize using only off-policy "winning images." Furthermore, we design a strategy for reference model selection that expands the exploration in the policy space. Notably, we do not simply treat reference samples as negative examples for learning. Instead, we design an anchor-based criterion to assess whether the reference samples are likely to be winning or losing images, allowing the model to selectively learn from the generated reference samples. This approach mitigates performance degradation caused by the uncertainty in reference sample quality. We validate SePPO across both text-to-image and text-to-video benchmarks. SePPO surpasses all previous approaches on the text-to-image benchmarks and also demonstrates outstanding performance on the text-to-video benchmarks. Code will be released in https://github.com/DwanZhang-AI/SePPO.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

In-context learning is a promising approach for online policy learning of offline reinforcement learning (RL) methods, which can be achieved at inference time without gradient optimization. However, this method is hindered by significant computational costs resulting from the gathering of large training trajectory sets and the need to train large Transformer models. We address this challenge by introducing an In-context Exploration-Exploitation (ICEE) algorithm, designed to optimize the efficiency of in-context policy learning. Unlike existing models, ICEE performs an exploration-exploitation trade-off at inference time within a Transformer model, without the need for explicit Bayesian inference. Consequently, ICEE can solve Bayesian optimization problems as efficiently as Gaussian process biased methods do, but in significantly less time. Through experiments in grid world environments, we demonstrate that ICEE can learn to solve new RL tasks using only tens of episodes, marking a substantial improvement over the hundreds of episodes needed by the previous in-context learning method.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

Mirror descent (MD), a well-known first-order method in constrained convex optimization, has recently been shown as an important tool to analyze trust-region algorithms in reinforcement learning (RL). However, there remains a considerable gap between such theoretically analyzed algorithms and the ones used in practice. Inspired by this, we propose an efficient RL algorithm, called {\em mirror descent policy optimization} (MDPO). MDPO iteratively updates the policy by {\em approximately} solving a trust-region problem, whose objective function consists of two terms: a linearization of the standard RL objective and a proximity term that restricts two consecutive policies to be close to each other. Each update performs this approximation by taking multiple gradient steps on this objective function. We derive {\em on-policy} and {\em off-policy} variants of MDPO, while emphasizing important design choices motivated by the existing theory of MD in RL. We highlight the connections between on-policy MDPO and two popular trust-region RL algorithms: TRPO and PPO, and show that explicitly enforcing the trust-region constraint is in fact {\em not} a necessity for high performance gains in TRPO. We then show how the popular soft actor-critic (SAC) algorithm can be derived by slight modifications of off-policy MDPO. Overall, MDPO is derived from the MD principles, offers a unified approach to viewing a number of popular RL algorithms, and performs better than or on-par with TRPO, PPO, and SAC in a number of continuous control tasks. Code is available at https://github.com/manantomar/Mirror-Descent-Policy-Optimization.

Large language models (LLMs) are increasingly deployed in multi-agent systems (MAS) as components of collaborative intelligence, where peer interactions dynamically shape individual decision-making. Although prior work has focused on conformity bias, we extend the analysis to examine how LLMs form trust from previous impressions, resist misinformation, and integrate peer input during interaction, key factors for achieving collective intelligence under complex social dynamics. We present KAIROS, a benchmark simulating quiz contests with peer agents of varying reliability, offering fine-grained control over conditions such as expert-novice roles, noisy crowds, and adversarial peers. LLMs receive both historical interactions and current peer responses, allowing systematic investigation into how trust, peer action, and self-confidence influence decisions. As for mitigation strategies, we evaluate prompting, supervised fine-tuning, and reinforcement learning, Group Relative Policy Optimisation (GRPO), across multiple models. Our results reveal that GRPO with multi-agent context combined with outcome-based rewards and unconstrained reasoning achieves the best overall performance, but also decreases the robustness to social influence compared to Base models. The code and datasets are available at: https://github.com/declare-lab/KAIROS.

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

Policy Optimization (PO) is one of the most popular methods in Reinforcement Learning (RL). Thus, theoretical guarantees for PO algorithms have become especially important to the RL community. In this paper, we study PO in adversarial MDPs with a challenge that arises in almost every real-world application -- delayed bandit feedback. We give the first near-optimal regret bounds for PO in tabular MDPs, and may even surpass state-of-the-art (which uses less efficient methods). Our novel Delay-Adapted PO (DAPO) is easy to implement and to generalize, allowing us to extend our algorithm to: (i) infinite state space under the assumption of linear Q-function, proving the first regret bounds for delayed feedback with function approximation. (ii) deep RL, demonstrating its effectiveness in experiments on MuJoCo domains.

Discovering achievements with a hierarchical structure on procedurally generated environments poses a significant challenge. This requires agents to possess a broad range of abilities, including generalization and long-term reasoning. Many prior methods are built upon model-based or hierarchical approaches, with the belief that an explicit module for long-term planning would be beneficial for learning hierarchical achievements. However, these methods require an excessive amount of environment interactions or large model sizes, limiting their practicality. In this work, we identify that proximal policy optimization (PPO), a simple and versatile model-free algorithm, outperforms the prior methods with recent implementation practices. Moreover, we find that the PPO agent can predict the next achievement to be unlocked to some extent, though with low confidence. Based on this observation, we propose a novel contrastive learning method, called achievement distillation, that strengthens the agent's capability to predict the next achievement. Our method exhibits a strong capacity for discovering hierarchical achievements and shows state-of-the-art performance on the challenging Crafter environment using fewer model parameters in a sample-efficient regime.

Large language models (LLMs) have demonstrated remarkable reasoning abilities in complex tasks, often relying on Chain-of-Thought (CoT) reasoning. However, due to their autoregressive token-level generation, the reasoning process is largely constrained to local decision-making and lacks global planning. This limitation frequently results in redundant, incoherent, or inaccurate reasoning, which significantly degrades overall performance. Existing approaches, such as tree-based algorithms and reinforcement learning (RL), attempt to address this issue but suffer from high computational costs and often fail to produce optimal reasoning trajectories. To tackle this challenge, we propose Plan-Then-Action Enhanced Reasoning with Group Relative Policy Optimization PTA-GRPO, a two-stage framework designed to improve both high-level planning and fine-grained CoT reasoning. In the first stage, we leverage advanced LLMs to distill CoT into compact high-level guidance, which is then used for supervised fine-tuning (SFT). In the second stage, we introduce a guidance-aware RL method that jointly optimizes the final output and the quality of high-level guidance, thereby enhancing reasoning effectiveness. We conduct extensive experiments on multiple mathematical reasoning benchmarks, including MATH, AIME2024, AIME2025, and AMC, across diverse base models such as Qwen2.5-7B-Instruct, Qwen3-8B, Qwen3-14B, and LLaMA3.2-3B. Experimental results demonstrate that PTA-GRPO consistently achieves stable and significant improvements across different models and tasks, validating its effectiveness and generalization.

Reinforcement learning (RL)-based fine-tuning has emerged as a powerful approach for aligning diffusion models with black-box objectives. Proximal policy optimization (PPO) is the most popular choice of method for policy optimization. While effective in terms of performance, PPO is highly sensitive to hyper-parameters and involves substantial computational overhead. REINFORCE, on the other hand, mitigates some computational complexities such as high memory overhead and sensitive hyper-parameter tuning, but has suboptimal performance due to high-variance and sample inefficiency. While the variance of the REINFORCE can be reduced by sampling multiple actions per input prompt and using a baseline correction term, it still suffers from sample inefficiency. To address these challenges, we systematically analyze the efficiency-effectiveness trade-off between REINFORCE and PPO, and propose leave-one-out PPO (LOOP), a novel RL for diffusion fine-tuning method. LOOP combines variance reduction techniques from REINFORCE, such as sampling multiple actions per input prompt and a baseline correction term, with the robustness and sample efficiency of PPO via clipping and importance sampling. Our results demonstrate that LOOP effectively improves diffusion models on various black-box objectives, and achieves a better balance between computational efficiency and performance.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

Function calling capabilities are crucial for deploying Large Language Models in real-world applications, yet current training approaches fail to develop robust reasoning strategies. Supervised fine-tuning produces models that rely on superficial pattern matching, while standard reinforcement learning methods struggle with the complex action space of structured function calls. We present a novel reinforcement learning framework designed to enhance group relative policy optimization through strategic entropy based exploration specifically tailored for function calling tasks. Our approach addresses three critical challenges in function calling: insufficient exploration during policy learning, lack of structured reasoning in chain-of-thought generation, and inadequate verification of parameter extraction. Our two-stage data preparation pipeline ensures high-quality training samples through iterative LLM evaluation and abstract syntax tree validation. Extensive experiments on the Berkeley Function Calling Leaderboard demonstrate that this framework achieves state-of-the-art performance among open-source models with 86.02\% overall accuracy, outperforming standard GRPO by up to 6\% on complex multi-function scenarios. Notably, our method shows particularly strong improvements on code-pretrained models, suggesting that structured language generation capabilities provide an advantageous starting point for reinforcement learning in function calling tasks. We will release all the code, models and dataset to benefit the community.

We present the LLM Economist, a novel framework that uses agent-based modeling to design and assess economic policies in strategic environments with hierarchical decision-making. At the lower level, bounded rational worker agents -- instantiated as persona-conditioned prompts sampled from U.S. Census-calibrated income and demographic statistics -- choose labor supply to maximize text-based utility functions learned in-context. At the upper level, a planner agent employs in-context reinforcement learning to propose piecewise-linear marginal tax schedules anchored to the current U.S. federal brackets. This construction endows economic simulacra with three capabilities requisite for credible fiscal experimentation: (i) optimization of heterogeneous utilities, (ii) principled generation of large, demographically realistic agent populations, and (iii) mechanism design -- the ultimate nudging problem -- expressed entirely in natural language. Experiments with populations of up to one hundred interacting agents show that the planner converges near Stackelberg equilibria that improve aggregate social welfare relative to Saez solutions, while a periodic, persona-level voting procedure furthers these gains under decentralized governance. These results demonstrate that large language model-based agents can jointly model, simulate, and govern complex economic systems, providing a tractable test bed for policy evaluation at the societal scale to help build better civilizations.

The process of revising (or constructing) a policy at execution time -- known as decision-time planning -- has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.

In multi-agent reinforcement learning, the behaviors that agents learn in a single Markov Game (MG) are typically confined to the given agent number. Every single MG induced by varying the population may possess distinct optimal joint strategies and game-specific knowledge, which are modeled independently in modern multi-agent reinforcement learning algorithms. In this work, our focus is on creating agents that can generalize across population-varying MGs. Instead of learning a unimodal policy, each agent learns a policy set comprising effective strategies across a variety of games. To achieve this, we propose Meta Representations for Agents (MRA) that explicitly models the game-common and game-specific strategic knowledge. By representing the policy sets with multi-modal latent policies, the game-common strategic knowledge and diverse strategic modes are discovered through an iterative optimization procedure. We prove that by approximately maximizing the resulting constrained mutual information objective, the policies can reach Nash Equilibrium in every evaluation MG when the latent space is sufficiently large. When deploying MRA in practical settings with limited latent space sizes, fast adaptation can be achieved by leveraging the first-order gradient information. Extensive experiments demonstrate the effectiveness of MRA in improving training performance and generalization ability in challenging evaluation games.

Language models as intelligent agents push the boundaries of sequential decision-making agents but struggle with limited knowledge of environmental dynamics and exponentially huge action space. Recent efforts like GLAM and TWOSOME manually constrain the action space to a restricted subset and employ reinforcement learning to align agents' knowledge with specific environments. However, they overlook fine-grained credit assignments for intra-action tokens, which is essential for efficient language agent optimization, and rely on human's prior knowledge to restrict action space. This paper proposes decomposing language agent optimization from the action level to the token level, offering finer supervision for each intra-action token and manageable optimization complexity in environments with unrestricted action spaces. Beginning with the simplification of flattening all actions, we theoretically explore the discrepancies between action-level optimization and this naive token-level optimization. We then derive the Bellman backup with Action Decomposition (BAD) to integrate credit assignments for both intra-action and inter-action tokens, effectively eliminating the discrepancies. Implementing BAD within the PPO algorithm, we introduce Policy Optimization with Action Decomposition (POAD). POAD benefits from a finer-grained credit assignment process and lower optimization complexity, leading to enhanced learning efficiency and generalization abilities in aligning language agents with interactive environments. We validate POAD across diverse testbeds, with results affirming the advantages of our approach and the correctness of our theoretical analysis.

Fairness, especially group fairness, is an important consideration in the context of machine learning systems. The most commonly adopted group fairness-enhancing techniques are in-processing methods that rely on a mixture of a fairness objective (e.g., demographic parity) and a task-specific objective (e.g., cross-entropy) during the training process. However, when data arrives in an online fashion -- one instance at a time -- optimizing such fairness objectives poses several challenges. In particular, group fairness objectives are defined using expectations of predictions across different demographic groups. In the online setting, where the algorithm has access to a single instance at a time, estimating the group fairness objective requires additional storage and significantly more computation (e.g., forward/backward passes) than the task-specific objective at every time step. In this paper, we propose Aranyani, an ensemble of oblique decision trees, to make fair decisions in online settings. The hierarchical tree structure of Aranyani enables parameter isolation and allows us to efficiently compute the fairness gradients using aggregate statistics of previous decisions, eliminating the need for additional storage and forward/backward passes. We also present an efficient framework to train Aranyani and theoretically analyze several of its properties. We conduct empirical evaluations on 5 publicly available benchmarks (including vision and language datasets) to show that Aranyani achieves a better accuracy-fairness trade-off compared to baseline approaches.

When reward functions are hand-designed, deep reinforcement learning algorithms often suffer from reward misspecification, causing them to learn suboptimal policies in terms of the intended task objectives. In the single-agent case, inverse reinforcement learning (IRL) techniques attempt to address this issue by inferring the reward function from expert demonstrations. However, in multi-agent problems, misalignment between the learned and true objectives is exacerbated due to increased environment non-stationarity and variance that scales with multiple agents. As such, in multi-agent general-sum games, multi-agent IRL algorithms have difficulty balancing cooperative and competitive objectives. To address these issues, we propose Multi-Agent Marginal Q-Learning from Demonstrations (MAMQL), a novel sample-efficient framework for multi-agent IRL. For each agent, MAMQL learns a critic marginalized over the other agents' policies, allowing for a well-motivated use of Boltzmann policies in the multi-agent context. We identify a connection between optimal marginalized critics and single-agent soft-Q IRL, allowing us to apply a direct, simple optimization criterion from the single-agent domain. Across our experiments on three different simulated domains, MAMQL significantly outperforms previous multi-agent methods in average reward, sample efficiency, and reward recovery by often more than 2-5x. We make our code available at https://sites.google.com/view/mamql .

We study why Tool-Integrated Reasoning (TIR) makes Large Language Models (LLMs) more capable. While LLMs integrated with tools like Python code interpreters show great promise, a principled theory explaining why this paradigm is effective has been missing. This work provides the first formal proof that TIR fundamentally expands an LLM's capabilities. We demonstrate that tools enable a strict expansion of the model's empirical and feasible support, breaking the capability ceiling of pure-text models by unlocking problem-solving strategies that are otherwise impossible or intractably verbose. To guide model behavior without compromising training stability and performance, we also introduce Advantage Shaping Policy Optimization (ASPO), a novel algorithm that directly modifies the advantage function to guide the policy behavior. We conduct comprehensive experiments on challenging mathematical benchmarks, leveraging a Python interpreter as the external tool. Our results show that the TIR model decisively outperforms its pure-text counterpart on the pass@k metric. Crucially, this advantage is not confined to computationally-intensive problems but extends to those requiring significant abstract insight. We further identify the emergent cognitive patterns that illustrate how models learn to think with tools. Finally, we report improved tool usage behavior with early code invocation and much more interactive turns with ASPO. Overall, our work provides the first principled explanation for TIR's success, shifting the focus from the mere fact that tools work to why and how they enable more powerful reasoning.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

Reinforcement learning (RL) has emerged as a promising strategy for finetuning small language models (SLMs) to solve targeted tasks such as math and coding. However, RL algorithms tend to be resource-intensive, taking a significant amount of time to train. We propose RAPID, a novel RL algorithm that can substantially reduce the running time of RL. Our key insight is that RL tends to be costly due to the need to perform both inference and backpropagation during training. To maximize use of computational resources, our algorithm performs inference in large batches, and then performs off-policy policy gradient updates in mini-batches. For off-policy updates, we incorporate group advantage estimation into the policy gradient algorithm, and derive an importance weighted estimator to correct for the bias arising from off-policy learning. Our experiments demonstrate that our algorithm can reduce running time by 11%-34% on three benchmarks compared to state-of-the-art RL algorithms while maintaining similar or better accuracy.

Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to address this, employing a closed-loop system where LLMs iteratively refine code based on empirical performance feedback from an execution sandbox. We explore three training strategies: Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and Group Relative Policy Optimization~(GRPO). Experiments on our Venus dataset and the APPS benchmark show that SFT and DPO rapidly saturate in efficiency gains. In contrast, GRPO, using reinforcement learning (RL) with execution feedback, continuously optimizes code performance, significantly boosting both pass@1 (from 47% to 62%) and the likelihood of outperforming human submissions in efficiency (from 31% to 45%). Our work demonstrates effective test-time code efficiency improvement and critically reveals the power of RL in teaching LLMs to truly self-improve code efficiency.

Large reasoning models achieve remarkable performance through extensive chain-of-thought generation, yet exhibit significant computational inefficiency by applying uniform reasoning strategies regardless of problem complexity. We present Hierarchical Budget Policy Optimization (HBPO), a reinforcement learning framework that enables models to learn problem-specific reasoning depths without sacrificing capability. HBPO addresses the fundamental challenge of exploration space collapse in efficiency-oriented training, where penalties on long output length systematically bias models away from necessary long reasoning paths. Through hierarchical budget exploration, our approach partitions rollout samples into multiple subgroups with distinct token budgets, aiming to enable efficient resource allocation while preventing degradation of capability. We introduce differentiated reward mechanisms that create budget-aware incentives aligned with the complexity of the problem, allowing models to discover natural correspondences between task requirements and computational effort. Extensive experiments demonstrate that HBPO reduces average token usage by up to 60.6% while improving accuracy by 3.14% across four reasoning benchmarks. Unlike existing methods that impose external constraints or rely on discrete mode selection, HBPO exhibits emergent adaptive behavior where models automatically adjust reasoning depth based on problem complexity. Our results suggest that reasoning efficiency and capability are not inherently conflicting, and can be simultaneously optimized through appropriately structured hierarchical training that preserves exploration diversity.

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Multi-Objective Reinforcement Learning (MORL) is a generalization of traditional Reinforcement Learning (RL) that aims to optimize multiple, often conflicting objectives simultaneously rather than focusing on a single reward. This approach is crucial in complex decision-making scenarios where agents must balance trade-offs between various goals, such as maximizing performance while minimizing costs. We consider the problem of MORL where the objectives are combined using a non-linear scalarization function. Just like in standard RL, policy gradient methods (PGMs) are amongst the most effective for handling large and continuous state-action spaces in MORL. However, existing PGMs for MORL suffer from high sample inefficiency, requiring large amounts of data to be effective. Previous attempts to solve this problem rely on overly strict assumptions, losing PGMs' benefits in scalability to large state-action spaces. In this work, we address the issue of sample efficiency by implementing variance-reduction techniques to reduce the sample complexity of policy gradients while maintaining general assumptions.

We focus on developing efficient and reliable policy optimization strategies for robot learning with real-world data. In recent years, policy gradient methods have emerged as a promising paradigm for training control policies in simulation. However, these approaches often remain too data inefficient or unreliable to train on real robotic hardware. In this paper we introduce a novel policy gradient-based policy optimization framework which systematically leverages a (possibly highly simplified) first-principles model and enables learning precise control policies with limited amounts of real-world data. Our approach 1) uses the derivatives of the model to produce sample-efficient estimates of the policy gradient and 2) uses the model to design a low-level tracking controller, which is embedded in the policy class. Theoretical analysis provides insight into how the presence of this feedback controller addresses overcomes key limitations of stand-alone policy gradient methods, while hardware experiments with a small car and quadruped demonstrate that our approach can learn precise control strategies reliably and with only minutes of real-world data.

Large language models split into two families: reasoning-centric LLMs, which strengthen internal chain-of-thought reasoning but cannot invoke external tools, and agentic LLMs, which learn to interact with environments and leverage tools but often lag in deep reasoning. This divide arises from fundamentally different training objectives, leading to mismatched strengths and inefficiency on simple queries, where both families tend to overthink or over-call tools. In this work, we present Adaptive Agent Foundation Model (A^2FM), a unified framework that follows a route-then-align principle: the model first learns task-aware routing and then aligns mode-specific trajectories under a shared backbone. To address the inefficiency gap, we introduce a third mode-instant-that handles simple queries directly, preventing unnecessary reasoning or tool calls while complementing the agentic and reasoning modes. To jointly enhance accuracy and efficiency, we propose Adaptive Policy Optimization (APO), which enforces adaptive sampling across modes and applies a cost-regularized reward. On the 32B scale, A^2FM achieves 13.4% on BrowseComp, 70.4% on AIME25, and 16.7% on HLE, setting new SOTA among comparable models and performing competitively with frontier LLMs across agentic, reasoning, and general benchmarks. Notably, the adaptive execution achieves a cost of pass of only $0.00487 per correct answer-cutting cost by 45.2% relative to reasoning and 33.5% relative to agentic, thus delivering substantially higher cost efficiency while maintaining comparable accuracy.

Training large language models (LLMs) as interactive agents for controlling graphical user interfaces (GUIs) presents a unique challenge to optimize long-horizon action sequences with multimodal feedback from complex environments. While recent works have advanced multi-turn reinforcement learning (RL) for reasoning and tool-using capabilities in LLMs, their application to GUI-based agents remains relatively underexplored due to the difficulty of sparse rewards, delayed feedback, and high rollout costs. In this paper, we investigate end-to-end policy optimization for vision-language-based GUI agents with the aim of improving performance on complex, long-horizon computer tasks. We propose Agentic Replay Policy Optimization (ARPO), an end-to-end RL approach that augments Group Relative Policy Optimization (GRPO) with a replay buffer to reuse the successful experience across training iterations. To further stabilize the training process, we propose a task selection strategy that filters tasks based on baseline agent performance, allowing the agent to focus on learning from informative interactions. Additionally, we compare ARPO with offline preference optimization approaches, highlighting the advantages of policy-based methods in GUI environments. Experiments on the OSWorld benchmark demonstrate that ARPO achieves competitive results, establishing a new performance baseline for LLM-based GUI agents trained via reinforcement learning. Our findings underscore the effectiveness of reinforcement learning for training multi-turn, vision-language GUI agents capable of managing complex real-world UI interactions. Codes and models:https://github.com/dvlab-research/ARPO.git.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that the interpretable nature of language can often provide a much richer learning medium for LLMs, compared with policy gradients derived from sparse, scalar rewards. To test this, we introduce GEPA (Genetic-Pareto), a prompt optimizer that thoroughly incorporates natural language reflection to learn high-level rules from trial and error. Given any AI system containing one or more LLM prompts, GEPA samples system-level trajectories (e.g., reasoning, tool calls, and tool outputs) and reflects on them in natural language to diagnose problems, propose and test prompt updates, and combine complementary lessons from the Pareto frontier of its own attempts. As a result of GEPA's design, it can often turn even just a few rollouts into a large quality gain. Across four tasks, GEPA outperforms GRPO by 10% on average and by up to 20%, while using up to 35x fewer rollouts. GEPA also outperforms the leading prompt optimizer, MIPROv2, by over 10% across two LLMs, and demonstrates promising results as an inference-time search strategy for code optimization.

Large Language Models (LLMs) exhibit robust problem-solving capabilities for diverse tasks. However, most LLM-based agents are designed as specific task solvers with sophisticated prompt engineering, rather than agents capable of learning and evolving through interactions. These task solvers necessitate manually crafted prompts to inform task rules and regulate LLM behaviors, inherently incapacitating to address complex dynamic scenarios e.g., large interactive games. In light of this, we propose Agent-Pro: an LLM-based Agent with Policy-level Reflection and Optimization that can learn a wealth of expertise from interactive experiences and progressively elevate its behavioral policy. Specifically, it involves a dynamic belief generation and reflection process for policy evolution. Rather than action-level reflection, Agent-Pro iteratively reflects on past trajectories and beliefs, fine-tuning its irrational beliefs for a better policy. Moreover, a depth-first search is employed for policy optimization, ensuring continual enhancement in policy payoffs. Agent-Pro is evaluated across two games: Blackjack and Texas Hold'em, outperforming vanilla LLM and specialized models. Our results show Agent-Pro can learn and evolve in complex and dynamic scenes, which also benefits numerous LLM-based applications.

Traditional reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed Self-Play Preference Optimization (SPPO), approximates the Nash equilibrium through iterative policy updates and enjoys theoretical convergence guarantee. Our method can effectively increase the log-likelihood of the chosen response and decrease that of the rejected response, which cannot be trivially achieved by symmetric pairwise loss such as Direct Preference Optimization (DPO) and Identity Preference Optimization (IPO). In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length-controlled win-rate of 28.53% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench and the Open LLM Leaderboard. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement learning can only be generalized to the fully centralized setting, because such approaches rely on the global symmetry in the full state-action spaces, and these can result in correspondences across agents. To encode such symmetries while still allowing distributed execution we propose a factorization that decomposes global symmetries into local transformations. Our proposed factorization allows for distributing the computation that enforces global symmetries over local agents and local interactions. We introduce a multi-agent equivariant policy network based on this factorization. We show empirically on symmetric multi-agent problems that globally symmetric distributable policies improve data efficiency compared to non-equivariant baselines.

Modern Tabletop Games present various interesting challenges for Multi-agent Reinforcement Learning. In this paper, we introduce PyTAG, a new framework that supports interacting with a large collection of games implemented in the Tabletop Games framework. In this work we highlight the challenges tabletop games provide, from a game-playing agent perspective, along with the opportunities they provide for future research. Additionally, we highlight the technical challenges that involve training Reinforcement Learning agents on these games. To explore the Multi-agent setting provided by PyTAG we train the popular Proximal Policy Optimisation Reinforcement Learning algorithm using self-play on a subset of games and evaluate the trained policies against some simple agents and Monte-Carlo Tree Search implemented in the Tabletop Games framework.

Reinforcement learning is essential for neural architecture search and hyperparameter optimization, but the conventional approaches impede widespread use due to prohibitive time and computational costs. Inspired by DeepSeek-V3 multi-token prediction architecture, we propose Sequential Policy Gradient modeling (SPG), a novel trajectory generation paradigm for lightweight online hyperparameter optimization. In contrast to conventional policy gradient methods, SPG extends the base model with temporary modules, enabling it to generate state-action (padded) trajectories in a single forward pass. Our experiments demonstrate that models gain performance when retrained with SPG on their original datasets and also outperform standard transfer fine-tuning. We evaluate on five datasets spanning computer vision (ImageNet, COCO), natural language processing (GLUE, SQuAD), and audio (SUPERB) to assess the industrial applicability of SPG. The proposed method demonstrates consistent improvements across widely adopted models, achieving performance gains of +0.2sim7%, with significantly low computational costs. Fully reproducible code and pre-trained models: https://huggingface.co/UniversalAlgorithmic/SPG.

Large reasoning models have achieved remarkable performance through extended chain-of-thought sequences, yet this computational freedom leads to excessive token generation even for simple problems. We present Length-Adaptive Policy Optimization (LAPO), a novel framework that transforms reasoning length control from an external constraint into an intrinsic model capability. Unlike existing approaches that impose rigid limits or rely on post-hoc interventions, LAPO enables models to internalize an understanding of appropriate reasoning depth through a two-stage reinforcement learning process. In the first stage, models learn natural reasoning patterns by discovering the statistical distribution of successful solution lengths. The second stage leverages these patterns as meta-cognitive guidance, embedding them directly within the model's reasoning context to ensure inference-time flexibility. Experiments on mathematical reasoning benchmarks demonstrate that LAPO reduces token usage by up to 40.9\% while improving accuracy by 2.3\%. Our analysis reveals that models trained with LAPO develop emergent abilities to allocate computational resources based on problem complexity, achieving efficient reasoning without sacrificing quality.

Optimizing discrete diffusion model (DDM) with rewards remains a challenge: the non-autoregressive paradigm makes importance sampling intractable and rollout complex, puzzling reinforcement learning methods such as Group Relative Policy Optimization (GRPO). In this study, we introduce MaskGRPO, the first viable approach to enable scalable multimodal reinforcement learning in discrete diffusion with effective importance sampling and modality-specific adaptations. To this end, we first clarify the theoretical foundation for DDMs, which facilitates building an importance estimator that captures valuable token fluctuation for gradient updates. We then delicately tailored the rollout method for visual sequences, which yields diverse completions and reliable optimization gradients. Upon math reasoning, coding, and visual generation benchmarks, MaskGRPO brings more stable and efficient updates, leading to stronger reasoning performance and better generation quality. This study establishes MaskGRPO as a systematic policy optimization approach and the first practical way for discretized visual diffusion.