Daily Papers

When confronted with complex problems, we tend to think slowly; conversely, for simple questions, we think quickly. Such a two-system thinking mechanism allows us to efficiently allocate cognitive resources, enabling quick decision-making for straightforward issues while reserving deeper analytical thinking for more intricate challenges. However, existing reasoning-oriented visual language models (VLMs), whether trained with explicit chain-of-thought annotations or rule-based RL rewards, mainly pursue lengthy, detailed reasoning chains, which often lead to excessive computational costs. In this work, we propose a simple RL approach, which enables VLMs to automatically switch between fast and slow thinking modes depending on task difficulty. The approach consists of two stages: in the first stage, we label data as either requiring fast thinking or slow thinking based on the model output length, which is inspired by the observation that pre-trained VLMs typically produce answers of varying lengths for different types of questions; in the second stage, we train the model using GRPO along with the thinking mode labels to develop dual-mode thinking. Despite its simplicity, our model, named DualMindVLM, significantly outperforms the base model and achieves performance on par with state-of-the-art visual reasoning models, while maintaining exceptionally high token efficiency.

Improving performance on complex tasks and enabling interpretable decision making in large language models (LLMs), especially for clinical applications, requires effective reasoning. Yet this remains challenging without supervised fine-tuning (SFT) on costly chain-of-thought (CoT) data distilled from closed-source models (e.g., GPT-4o). In this work, we present AlphaMed, the first medical LLM to show that reasoning capability can emerge purely through reinforcement learning (RL), using minimalist rule-based rewards on public multiple-choice QA datasets, without relying on SFT or distilled CoT data. AlphaMed achieves state-of-the-art results on six medical QA benchmarks, outperforming models trained with conventional SFT+RL pipelines. On challenging benchmarks (e.g., MedXpert), AlphaMed even surpasses larger or closed-source models such as DeepSeek-V3-671B and Claude-3.5-Sonnet. To understand the factors behind this success, we conduct a comprehensive data-centric analysis guided by three questions: (i) Can minimalist rule-based RL incentivize reasoning without distilled CoT supervision? (ii) How do dataset quantity and diversity impact reasoning? (iii) How does question difficulty shape the emergence and generalization of reasoning? Our findings show that dataset informativeness is a key driver of reasoning performance, and that minimalist RL on informative, multiple-choice QA data is effective at inducing reasoning without CoT supervision. We also observe divergent trends across benchmarks, underscoring limitations in current evaluation and the need for more challenging, reasoning-oriented medical QA benchmarks.

Training tool-augmented LLMs has emerged as a promising approach to enhancing language models' capabilities for complex tasks. The current supervised fine-tuning paradigm relies on constructing extensive domain-specific datasets to train models. However, this approach often struggles to generalize effectively to unfamiliar or intricate tool-use scenarios. Recently, reinforcement learning (RL) paradigm can endow LLMs with superior reasoning and generalization abilities. In this work, we address a key question: Can the pure RL be used to effectively elicit a model's intrinsic reasoning capabilities and enhance the tool-agnostic generalization? We propose a dynamic generalization-guided reward design for rule-based RL, which progressively shifts rewards from exploratory to exploitative tool-use patterns. Based on this design, we introduce the Tool-Zero series models. These models are trained to enable LLMs to autonomously utilize general tools by directly scaling up RL from Zero models (i.e., base models without post-training). Experimental results demonstrate that our models achieve over 7% performance improvement compared to both SFT and RL-with-SFT models under the same experimental settings. These gains are consistently replicated across cross-dataset and intra-dataset evaluations, validating the effectiveness and robustness of our methods.

Search agents powered by Large Language Models (LLMs) have demonstrated significant potential in tackling knowledge-intensive tasks. Reinforcement learning (RL) has emerged as a powerful paradigm for training these agents to perform complex, multi-step reasoning. However, prior RL-based methods often rely on sparse or rule-based rewards, which can lead agents to commit to suboptimal or erroneous reasoning paths without the ability to recover. To address these limitations, we propose ReSeek, a novel self-correcting framework for training search agents. Our framework introduces a self-correction mechanism that empowers the agent to dynamically identify and recover from erroneous search paths during an episode. By invoking a special JUDGE action, the agent can judge the information and re-plan its search strategy. To guide this process, we design a dense, instructive process reward function, which decomposes into a correctness reward for retrieving factual information and a utility reward for finding information genuinely useful for the query. Furthermore, to mitigate the risk of data contamination in existing datasets, we introduce FictionalHot, a new and challenging benchmark with recently curated questions requiring complex reasoning. Being intuitively reasonable and practically simple, extensive experiments show that agents trained with ReSeek significantly outperform SOTA baselines in task success rate and path faithfulness.

Recent advances have shown success in eliciting strong reasoning abilities in multimodal large language models (MLLMs) through rule-based reinforcement learning (RL) with outcome rewards. However, this paradigm typically lacks supervision over the thinking process leading to the final outcome.As a result, the model may learn sub-optimal reasoning strategies, which can hinder its generalization ability. In light of this, we propose SophiaVL-R1, as an attempt to add reward signals for the thinking process in this paradigm. To achieve this, we first train a thinking reward model that evaluates the quality of the entire thinking process. Given that the thinking reward may be unreliable for certain samples due to reward hacking, we propose the Trust-GRPO method, which assigns a trustworthiness weight to the thinking reward during training. This weight is computed based on the thinking reward comparison of responses leading to correct answers versus incorrect answers, helping to mitigate the impact of potentially unreliable thinking rewards. Moreover, we design an annealing training strategy that gradually reduces the thinking reward over time, allowing the model to rely more on the accurate rule-based outcome reward in later training stages. Experiments show that our SophiaVL-R1 surpasses a series of reasoning MLLMs on various benchmarks (e.g., MathVisita, MMMU), demonstrating strong reasoning and generalization capabilities. Notably, our SophiaVL-R1-7B even outperforms LLaVA-OneVision-72B on most benchmarks, despite the latter having 10 times more parameters. All code, models, and datasets are made publicly available at https://github.com/kxfan2002/SophiaVL-R1.

Recent advances in rule-based reinforcement learning (RL) have significantly improved the reasoning capability of language models (LMs) with rule-based rewards. However, existing RL methods -- such as GRPO, REINFORCE++, and RLOO -- often suffer from training instability, where large policy updates and improper clipping can lead to training collapse. To address this issue, we propose Clipped Policy Gradient Optimization with Policy Drift (CPGD), a novel algorithm designed to stabilize policy learning in LMs. CPGD introduces a policy drift constraint based on KL divergence to dynamically regularize policy updates, and leverages a clip mechanism on the logarithm of the ratio to prevent excessive policy updates. We provide theoretical justification for CPGD and demonstrate through empirical analysis that it mitigates the instability observed in prior approaches. Furthermore, we show that CPGD significantly improves performance while maintaining training stability. Our implementation balances theoretical rigor with practical usability, offering a robust alternative for RL in the post-training of LMs. We release our code at https://github.com/ModalMinds/MM-EUREKA.

The advancement of general-purpose artificial intelligence relies on large language models (LLMs) that excel across a wide range of tasks, from structured reasoning to creative generation. However, post-training methods like Supervised Fine-Tuning (SFT) often struggle with generalization, favoring memorization over transferable learning. In this work, we introduce Omni-Thinker, a unified reinforcement learning (RL) framework that enhances LLM performance across diverse tasks by combining rule-based verifiable rewards with generative preference signals via LLM-as-a-Judge evaluations. Our approach enables consistent optimization across task types and scales RL-based training to subjective domains. We further investigate training strategies, demonstrating that a curriculum-based progression that orders tasks from structured to open-ended improves performance and reduces forgetting. Experimental results across four domains reveal that curriculum learning improves performance by 5.2% over joint training and 9.1% over model merging. These results highlight the importance of task-aware sampling and hybrid supervision in scaling RL-based post-training for general-purpose LLMs.

Classification is a core task in machine learning. Recent research has shown that although Multimodal Large Language Models (MLLMs) are initially poor at image classification, fine-tuning them with an adequate amount of data can significantly enhance their performance, making them comparable to SOTA classification models. However, acquiring large-scale labeled data is expensive. In this paper, we explore few-shot MLLM classification fine-tuning. We found that SFT can cause severe overfitting issues and may even degrade performance over the zero-shot approach. To address this challenge, inspired by the recent successes in rule-based reinforcement learning, we propose CLS-RL, which uses verifiable signals as reward to fine-tune MLLMs. We discovered that CLS-RL outperforms SFT in most datasets and has a much higher average accuracy on both base-to-new and few-shot learning setting. Moreover, we observed a free-lunch phenomenon for CLS-RL; when models are fine-tuned on a particular dataset, their performance on other distinct datasets may also improve over zero-shot models, even if those datasets differ in distribution and class names. This suggests that RL-based methods effectively teach models the fundamentals of classification. Lastly, inspired by recent works in inference time thinking, we re-examine the `thinking process' during fine-tuning, a critical aspect of RL-based methods, in the context of visual classification. We question whether such tasks require extensive thinking process during fine-tuning, proposing that this may actually detract from performance. Based on this premise, we introduce the No-Thinking-CLS-RL method, which minimizes thinking processes during training by setting an equality accuracy reward. Our findings indicate that, with much less fine-tuning time, No-Thinking-CLS-RL method achieves superior in-domain performance and generalization capabilities than CLS-RL.

Reinforcement learning with verifiable rewards (RLVR) has enabled large language models (LLMs) to achieve remarkable breakthroughs in reasoning tasks with objective ground-truth answers, such as mathematics and code generation. However, a significant gap remains for non-verifiable tasks, like creative writing and open-ended dialogue, where quality assessment is inherently subjective and lacks definitive references. Existing approaches for these domains often rely on scalar reward models trained with human preferences, which suffer from limited generalization and are prone to reward hacking, such as over-explanation and length bias. In this work, we propose a unified RLVR-based training paradigm that bridges the gap between non-verifiable tasks and verifiable rewards. We introduce a writing-principle-based pairwise Generative Reward Model (GenRM) and a novel Bootstrapped Relative Policy Optimization (BRPO) algorithm. The pairwise writing GenRM leverages self-principled critique to transform subjective assessments into reliable, verifiable rewards, while BRPO enables dynamic, reference-free pairwise comparison by leveraging a bootstrapped response as temporary reference from within group rollouts during RL training. Our approach empowers LLMs to develop robust writing capabilities without supervised fine-tuning, as demonstrated by Writing-Zero, which shows consistent improvement and strong resistance to reward hacking compared to scalar reward baselines. Furthermore, our method achieves competitive results on both in-house and open-source writing benchmarks. Our findings suggest the potential to unify rule-based, reference-based, and reference-free reward modeling under the RLVR framework, thus paving the way for a comprehensive and scalable RL training paradigm applicable across all language tasks.

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor's outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a 9.02% gain on in-domain tasks and a 5.70% gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

Reinforcement learning (RL) with rule-based rewards has demonstrated strong potential in enhancing the reasoning and generalization capabilities of vision-language models (VLMs) and large language models (LLMs), while reducing computational overhead. However, its application in medical imaging remains underexplored. Existing reinforcement fine-tuning (RFT) approaches in this domain primarily target closed-ended visual question answering (VQA), limiting their applicability to real-world clinical reasoning. In contrast, open-ended medical VQA better reflects clinical practice but has received limited attention. While some efforts have sought to unify both formats via semantically guided RL, we observe that model-based semantic rewards often suffer from reward collapse, where responses with significant semantic differences receive similar scores. To address this, we propose ARMed (Adaptive Reinforcement for Medical Reasoning), a novel RL framework for open-ended medical VQA. ARMed first incorporates domain knowledge through supervised fine-tuning (SFT) on chain-of-thought data, then applies reinforcement learning with textual correctness and adaptive semantic rewards to enhance reasoning quality. We evaluate ARMed on six challenging medical VQA benchmarks. Results show that ARMed consistently boosts both accuracy and generalization, achieving a 32.64% improvement on in-domain tasks and an 11.65% gain on out-of-domain benchmarks. These results highlight the critical role of reward discriminability in medical RL and the promise of semantically guided rewards for enabling robust and clinically meaningful multimodal reasoning.

The recent DeepSeek-R1 has showcased the emergence of reasoning capabilities in LLMs through reinforcement learning (RL) with rule-based rewards. Building on this idea, we are the first to explore how rule-based RL can enhance the reasoning capabilities of multimodal large language models (MLLMs) for graphic user interface (GUI) action prediction tasks. To this end, we curate a small yet high-quality dataset of 136 challenging tasks, encompassing five common action types on mobile devices. We also introduce a unified rule-based action reward, enabling model optimization via policy-based algorithms such as Group Relative Policy Optimization (GRPO). Experimental results demonstrate that our proposed data-efficient model, UI-R1-3B, achieves substantial improvements on both in-domain (ID) and out-of-domain (OOD) tasks. Specifically, on the ID benchmark AndroidControl, the action type accuracy improves by 15%, while grounding accuracy increases by 10.3%, compared with the base model (i.e. Qwen2.5-VL-3B). On the OOD GUI grounding benchmark ScreenSpot-Pro, our model surpasses the base model by 6.0% and achieves competitive performance with larger models (e.g., OS-Atlas-7B), which are trained via supervised fine-tuning (SFT) on 76K data. These results underscore the potential of rule-based reinforcement learning to advance GUI understanding and control, paving the way for future research in this domain.

DeepSeek-R1 has shown that long chain-of-thought (CoT) reasoning can naturally emerge through a simple reinforcement learning (RL) framework with rule-based rewards, where the training may directly start from the base models-a paradigm referred to as zero RL training. Most recent efforts to reproduce zero RL training have primarily focused on the Qwen2.5 model series, which may not be representative as we find the base models already exhibit strong instruction-following and self-reflection abilities. In this work, we investigate zero RL training across 10 diverse base models, spanning different families and sizes including LLama3-8B, Mistral-7B/24B, DeepSeek-Math-7B, Qwen2.5-math-7B, and all Qwen2.5 models from 0.5B to 32B. Leveraging several key design strategies-such as adjusting format reward and controlling query difficulty-we achieve substantial improvements in both reasoning accuracy and response length across most settings. However, by carefully monitoring the training dynamics, we observe that different base models exhibit distinct patterns during training. For instance, the increased response length does not always correlate with the emergence of certain cognitive behaviors such as verification (i.e., the "aha moment"). Notably, we observe the "aha moment" for the first time in small models not from the Qwen family. We share the key designs that enable successful zero RL training, along with our findings and practices. To facilitate further research, we open-source the code, models, and analysis tools.

Reinforcement learning (RL) has significantly improved the reasoning ability of large language models. However, current reward models underperform in challenging reasoning scenarios and predominant RL training paradigms rely on rule-based or reference-based rewards, which impose two critical limitations: 1) the dependence on finely annotated reference answer to attain rewards; and 2) the requirement for constrained output format. These limitations fundamentally hinder further RL data scaling and sustained enhancement of model reasoning performance. To address these limitations, we propose a comprehensive framework for evaluating and improving the performance of reward models in complex reasoning scenarios. We first present a reasoning-oriented benchmark (Libra Bench), systematically constructed from a diverse collection of challenging mathematical problems and advanced reasoning models, to address the limitations of existing reward model benchmarks in reasoning scenarios. We further introduce a novel approach for improving the generative reward model via learning-to-think methodologies. Based on the proposed approach, we develop Libra-RM series, a collection of generative reward models with reasoning capabilities that achieve state-of-the-art results on various benchmarks. Comprehensive downstream experiments are conducted and the experimental results demonstrate the correlation between our Libra Bench and downstream application, and the potential of Libra-RM to further improve reasoning models with unlabeled data.

We investigate the potential of large language models (LLMs) to serve as efficient simulators for agentic search tasks in reinforcement learning (RL), thereby reducing dependence on costly interactions with external search engines. To this end, we first quantify the intrinsic search capability of LLMs via structured prompting and repeated sampling, which we term Self-Search. Our results reveal that LLMs exhibit strong scaling behavior with respect to the inference budget, achieving high pass@k on question-answering benchmarks, including the challenging BrowseComp task. Building on these observations, we introduce Self-Search RL (SSRL), which enhances LLMs' Self-Search capability through format-based and rule-based rewards. SSRL enables models to iteratively refine their knowledge utilization internally, without requiring access to external tools. Empirical evaluations demonstrate that SSRL-trained policy models provide a cost-effective and stable environment for search-driven RL training, reducing reliance on external search engines and facilitating robust sim-to-real transfer. We draw the following conclusions: 1) LLMs possess world knowledge that can be effectively elicited to achieve high performance; 2) SSRL demonstrates the potential of leveraging internal knowledge to reduce hallucination; 3) SSRL-trained models integrate seamlessly with external search engines without additional effort. Our findings highlight the potential of LLMs to support more scalable RL agent training.

Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning (RL) with simple rule-based rewards. However, existing zero-RL approaches are inherently ``on-policy'', limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. We introduce LUFFY (Learning to reason Under oFF-policY guidance), a framework that augments zero-RL with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Notably, we propose policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Remarkably, LUFFY achieves an over +7.0 average gain across six math benchmarks and an advantage of over +6.2 points in out-of-distribution tasks. It also substantially surpasses imitation-based supervised fine-tuning (SFT), particularly in generalization. Analysis shows LUFFY not only imitates effectively but also explores beyond demonstrations, offering a scalable path to train generalizable reasoning models with off-policy guidance.

While advancements in the reasoning abilities of LLMs have significantly enhanced their performance in solving mathematical problems, coding tasks, and general puzzles, their effectiveness in accurately adhering to instructions remains inconsistent, particularly with more complex directives. Our investigation identifies lazy reasoning during the thinking stage as the primary factor contributing to poor instruction adherence. To mitigate this issue, we propose a comprehensive framework designed to enable rigorous reasoning processes involving preview and self-checking, essential for satisfying strict instruction constraints. Specifically, we first generate instructions with complex constraints and apply a filtering process to obtain valid prompts, resulting in three distinct prompt datasets categorized as hard, easy, and pass. Then, we employ rejection sampling on the pass prompts to curate a small yet high-quality dataset, enabling a cold-start initialization of the model and facilitating its adaptation to effective reasoning patterns. Subsequently, we employ an entropy-preserving supervised fine-tuning (Entropy-SFT) strategy coupled with token-wise entropy-adaptive (TEA-RL) reinforcement learning guided by rule-based dense rewards. This approach encourages the model to transform its reasoning mechanism, ultimately fostering generalizable reasoning abilities that encompass preview and self-checking. Extensive experiments conducted on instruction-following benchmarks demonstrate remarkable performance improvements across various model scales. Notably, our Light-IF-32B model surpasses both larger open-source models such as DeepSeek-R1 and closed-source models like Doubao-1.6.

In online reinforcement learning (online RL), balancing exploration and exploitation is crucial for finding an optimal policy in a sample-efficient way. To achieve this, existing sample-efficient online RL algorithms typically consist of three components: estimation, planning, and exploration. However, in order to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as optimization within data-dependent level-sets or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called Maximize to Explore (MEX), which only needs to optimize unconstrainedly a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that MEX achieves a sublinear regret with general function approximations for Markov decision processes (MDP) and is further extendable to two-player zero-sum Markov games (MG). Meanwhile, we adapt deep RL baselines to design practical versions of MEX, in both model-free and model-based manners, which can outperform baselines by a stable margin in various MuJoCo environments with sparse rewards. Compared with existing sample-efficient online RL algorithms with general function approximations, MEX achieves similar sample efficiency while enjoying a lower computational cost and is more compatible with modern deep RL methods.

We present MM-Eureka, a multimodal reasoning model that successfully extends large-scale rule-based reinforcement learning (RL) to multimodal reasoning. While rule-based RL has shown remarkable success in improving LLMs' reasoning abilities in text domains, its application to multimodal settings has remained challenging. Our work reproduces key characteristics of text-based RL systems like DeepSeek-R1 in the multimodal space, including steady increases in accuracy reward and response length, and the emergence of reflection behaviors. We demonstrate that both instruction-tuned and pre-trained models can develop strong multimodal reasoning capabilities through rule-based RL without supervised fine-tuning, showing superior data efficiency compared to alternative approaches. We open-source our complete pipeline to foster further research in this area. We release all our codes, models, data, etc. at https://github.com/ModalMinds/MM-EUREKA

Multimodal Reward Models (MRMs) play a crucial role in enhancing the performance of Multimodal Large Language Models (MLLMs). While recent advancements have primarily focused on improving the model structure and training data of MRMs, there has been limited exploration into the effectiveness of long-term reasoning capabilities for reward modeling and how to activate these capabilities in MRMs. In this paper, we explore how Reinforcement Learning (RL) can be used to improve reward modeling. Specifically, we reformulate the reward modeling problem as a rule-based RL task. However, we observe that directly applying existing RL algorithms, such as Reinforce++, to reward modeling often leads to training instability or even collapse due to the inherent limitations of these algorithms. To address this issue, we propose the StableReinforce algorithm, which refines the training loss, advantage estimation strategy, and reward design of existing RL methods. These refinements result in more stable training dynamics and superior performance. To facilitate MRM training, we collect 200K preference data from diverse datasets. Our reward model, R1-Reward, trained using the StableReinforce algorithm on this dataset, significantly improves performance on multimodal reward modeling benchmarks. Compared to previous SOTA models, R1-Reward achieves a 8.4% improvement on the VL Reward-Bench and a 14.3% improvement on the Multimodal Reward Bench. Moreover, with more inference compute, R1-Reward's performance is further enhanced, highlighting the potential of RL algorithms in optimizing MRMs.

Recent progress in large-scale reinforcement learning (RL) has notably enhanced the reasoning capabilities of large language models (LLMs), especially in mathematical domains. However, current multimodal LLMs (MLLMs) for mathematical reasoning often rely on one-to-one image-text pairs and single-solution supervision, overlooking the diversity of valid reasoning perspectives and internal reflections. In this work, we introduce MathV-DP, a novel dataset that captures multiple diverse solution trajectories for each image-question pair, fostering richer reasoning supervision. We further propose Qwen-VL-DP, a model built upon Qwen-VL, fine-tuned with supervised learning and enhanced via group relative policy optimization (GRPO), a rule-based RL approach that integrates correctness discrimination and diversity-aware reward functions. Our method emphasizes learning from varied reasoning perspectives and distinguishing between correct yet distinct solutions. Extensive experiments on the MathVista's minitest and Math-V benchmarks demonstrate that Qwen-VL-DP significantly outperforms prior base MLLMs in both accuracy and generative diversity, highlighting the importance of incorporating diverse perspectives and reflective reasoning in multimodal mathematical reasoning.

Reinforcement learning from human feedback (RLHF) has become a powerful post-training paradigm for aligning large language models with human preferences. A core challenge in RLHF is constructing accurate reward signals, where the conventional Bradley-Terry reward models (BT RMs) often suffer from sensitivity to data size and coverage, as well as vulnerability to reward hacking. Generative reward models (GenRMs) offer a more robust alternative by generating chain-of-thought (CoT) rationales followed by a final reward. However, existing GenRMs rely on shallow, vertically scaled reasoning, limiting their capacity to handle nuanced or complex (e.g., reasoning-intensive) tasks. Moreover, their pairwise preference outputs are incompatible with standard RLHF algorithms that require pointwise reward signals. In this work, we introduce Think-RM, a training framework that enables long-horizon reasoning in GenRMs by modeling an internal thinking process. Rather than producing structured, externally provided rationales, Think-RM generates flexible, self-guided reasoning traces that support advanced capabilities such as self-reflection, hypothetical reasoning, and divergent reasoning. To elicit these reasoning abilities, we first warm-up the models by supervised fine-tuning (SFT) over long CoT data. We then further improve the model's long-horizon abilities by rule-based reinforcement learning (RL). In addition, we propose a novel pairwise RLHF pipeline that directly optimizes policies using pairwise preference rewards, eliminating the need for pointwise reward conversion and enabling more effective use of Think-RM outputs. Experiments show that Think-RM achieves state-of-the-art results on RM-Bench, outperforming both BT RM and vertically scaled GenRM by 8%. When combined with our pairwise RLHF pipeline, it demonstrates superior end-policy performance compared to traditional approaches.

Spatial reasoning remains a critical yet underdeveloped capability in existing vision-language models (VLMs), especially for Spatial Visual Question Answering (Spatial VQA) tasks that require understanding relative positions, distances, and object configurations. Inspired by the R1 paradigm introduced in DeepSeek-R1, which enhances reasoning in language models through rule-based reinforcement learning (RL), we propose SVQA-R1, the first framework to extend R1-style training to spatial VQA. In particular, we introduce Spatial-GRPO, a novel group-wise RL strategy that constructs view-consistent rewards by perturbing spatial relations between objects, e.g., mirror flipping, thereby encouraging the model to develop a consistent and grounded understanding of space. Our model, SVQA-R1, not only achieves dramatically improved accuracy on spatial VQA benchmarks but also exhibits interpretable reasoning paths even without using supervised fine-tuning (SFT) data. Extensive experiments and visualization demonstrate the effectiveness of SVQA-R1 across multiple spatial reasoning benchmarks.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

The recent DeepSeek-R1 release has demonstrated the immense potential of reinforcement learning (RL) in enhancing the general reasoning capabilities of large language models (LLMs). While DeepSeek-R1 and other follow-up work primarily focus on applying RL to competitive coding and math problems, this paper introduces SWE-RL, the first approach to scale RL-based LLM reasoning for real-world software engineering. Leveraging a lightweight rule-based reward (e.g., the similarity score between ground-truth and LLM-generated solutions), SWE-RL enables LLMs to autonomously recover a developer's reasoning processes and solutions by learning from extensive open-source software evolution data -- the record of a software's entire lifecycle, including its code snapshots, code changes, and events such as issues and pull requests. Trained on top of Llama 3, our resulting reasoning model, Llama3-SWE-RL-70B, achieves a 41.0% solve rate on SWE-bench Verified -- a human-verified collection of real-world GitHub issues. To our knowledge, this is the best performance reported for medium-sized (<100B) LLMs to date, even comparable to leading proprietary LLMs like GPT-4o. Surprisingly, despite performing RL solely on software evolution data, Llama3-SWE-RL has even emerged with generalized reasoning skills. For example, it shows improved results on five out-of-domain tasks, namely, function coding, library use, code reasoning, mathematics, and general language understanding, whereas a supervised-finetuning baseline even leads to performance degradation on average. Overall, SWE-RL opens up a new direction to improve the reasoning capabilities of LLMs through reinforcement learning on massive software engineering data.

As a fundamental task in machine learning, text classification plays a crucial role in many areas. With the rapid scaling of Large Language Models (LLMs), particularly through reinforcement learning (RL), there is a growing need for more capable discriminators. Consequently, advances in classification are becoming increasingly vital for enhancing the overall capabilities of LLMs. Traditional discriminative methods map text to labels but overlook LLMs' intrinsic generative strengths. Generative classification addresses this by prompting the model to directly output labels. However, existing studies still rely on simple SFT alone, seldom probing the interplay between training and inference prompts, and no work has systematically leveraged RL for generative text classifiers and unified SFT, RL, and inference-time prompting in one framework. We bridge this gap with GenCLS++, a framework that jointly optimizes SFT and RL while systematically exploring five high-level strategy dimensions-in-context learning variants, category definitions, explicit uncertainty labels, semantically irrelevant numeric labels, and perplexity-based decoding-during both training and inference. After an SFT "policy warm-up," we apply RL with a simple rule-based reward, yielding sizable extra gains. Across seven datasets, GenCLS++ achieves an average accuracy improvement of 3.46% relative to the naive SFT baseline; on public datasets, this improvement rises to 4.00%. Notably, unlike reasoning-intensive tasks that benefit from explicit thinking processes, we find that classification tasks perform better without such reasoning steps. These insights into the role of explicit reasoning provide valuable guidance for future LLM applications.

Multimodal Large Language Models (MLLMs) have demonstrated significant visual understanding capabilities, yet their fine-grained visual perception in complex real-world scenarios, such as densely crowded public areas, remains limited. Inspired by the recent success of reinforcement learning (RL) in both LLMs and MLLMs, in this paper, we explore how RL can enhance visual perception ability of MLLMs. Then we develop a novel RL-based framework, Deep Inspection and Perception with RL (DIP-R1) designed to enhance the visual perception capabilities of MLLMs, by comprehending complex scenes and looking through visual instances closely. DIP-R1 guides MLLMs through detailed inspection of visual scene via three simply designed rule-based reward modelings. First, we adopt a standard reasoning reward encouraging the model to include three step-by-step processes: 1) reasoning for understanding visual scenes, 2) observing for looking through interested but ambiguous regions, and 3) decision-making for predicting answer. Second, a variance-guided looking reward is designed to examine uncertain regions for the second observing process. It explicitly enables the model to inspect ambiguous areas, improving its ability to mitigate perceptual uncertainties. Third, we model a weighted precision-recall accuracy reward enhancing accurate decision-making. We explore its effectiveness across diverse fine-grained object detection data consisting of challenging real-world environments, such as densely crowded scenes. Built upon existing MLLMs, DIP-R1 achieves consistent and significant improvement across various in-domain and out-of-domain scenarios. It also outperforms various existing baseline models and supervised fine-tuning methods. Our findings highlight the substantial potential of integrating RL into MLLMs for enhancing capabilities in complex real-world perception tasks.

Supervised fine-tuning (SFT) and reinforcement learning (RL) are widely used post-training techniques for foundation models. However, their roles in enhancing model generalization capabilities remain unclear. This paper studies the difference between SFT and RL on generalization and memorization, focusing on text-based rule variants and visual variants. We introduce GeneralPoints, an arithmetic reasoning card game, and adopt V-IRL, a real-world navigation environment, to assess how models trained with SFT and RL generalize to unseen variants in both textual and visual domains. We show that RL, especially when trained with an outcome-based reward, generalizes across both rule-based textual and visual variants. SFT, in contrast, tends to memorize training data and struggles to generalize out-of-distribution scenarios. Further analysis reveals that RL improves the model's underlying visual recognition capabilities, contributing to its enhanced generalization in the visual domain. Despite RL's superior generalization, we show that SFT remains essential for effective RL training; SFT stabilizes the model's output format, enabling subsequent RL to achieve its performance gains. These findings demonstrates the capability of RL for acquiring generalizable knowledge in complex, multi-modal tasks.

In recent years, large language models (LLMs) have played an important role in automatic speech recognition (ASR) and text-to-speech (TTS) systems. While reinforcement learning (RL) has significantly enhanced LLM performance in text-based tasks, its application to ASR and TTS remains underexplored due to the complexity of training audio-based models. In this study, we propose a lightweight RL framework tailored for audio-based LLMs that can process audio inputs and generate audio outputs. Based on this framework, we evaluate the effectiveness of reinforcement learning on both ASR and TTS tasks. For the ASR task, we experiment with different rule-based reward functions within the Group Relative Policy Optimization (GRPO) framework and investigate the impact of RL data construction. For the TTS task, we compare GRPO with Differentiable Reward Optimization (DiffRO) and further combine the two approaches to achieve improved performance. Our experiments demonstrate that RL can significantly enhance the performance of both ASR and TTS systems, even with limited training data and a small number of optimization steps.

Scaling up test-time compute, by generating multiple independent solutions and selecting or aggregating among them, has become a central paradigm for improving large language models (LLMs) on challenging reasoning tasks. While most prior work relies on simple majority voting or reward model ranking to aggregate solutions, these approaches may only yield limited benefits. In this work, we propose to learn aggregation as an explicit reasoning skill: given a set of candidate solutions, we train an aggregator model to review, reconcile, and synthesize a final, correct answer using reinforcement learning from verifiable rewards. A key ingredient is careful balancing of easy and hard training examples, allowing the model to learn both to recover minority-but-correct answers as well as easy majority-correct answers. Empirically, we find our method, AggLM, outperforms both strong rule-based and reward-model baselines, across multiple benchmarks. Furthermore, it generalizes effectively to solutions from differing models, including stronger ones than contained in the training data, all while requiring substantially fewer tokens than majority voting with larger numbers of solutions.

Reinforcement Learning (RL) has become a powerful tool for enhancing the reasoning abilities of large language models (LLMs) by optimizing their policies with reward signals. Yet, RL's success relies on the reliability of rewards, which are provided by verifiers. In this paper, we expose and analyze a widespread problem--false negatives--where verifiers wrongly reject correct model outputs. Our in-depth study of the Big-Math-RL-Verified dataset reveals that over 38% of model-generated responses suffer from false negatives, where the verifier fails to recognize correct answers. We show, both empirically and theoretically, that these false negatives severely impair RL training by depriving the model of informative gradient signals and slowing convergence. To mitigate this, we propose tinyV, a lightweight LLM-based verifier that augments existing rule-based methods, which dynamically identifies potential false negatives and recovers valid responses to produce more accurate reward estimates. Across multiple math-reasoning benchmarks, integrating TinyV boosts pass rates by up to 10% and accelerates convergence relative to the baseline. Our findings highlight the critical importance of addressing verifier false negatives and offer a practical approach to improve RL-based fine-tuning of LLMs. Our code is available at https://github.com/uw-nsl/TinyV.

We investigate how to teach large language models (LLMs) to perform scientific reasoning by leveraging expert discussions as a learning signal. Focusing on the genomics domain, we develop an automated pipeline to extract trainable data and introduce Genome-Bench, a new benchmark constructed from over a decade of scientific forum discussions on genome engineering. Our pipeline transforms raw interactions into a reinforcement learning-friendly multiple-choice questions format, supported by 3000+ high-quality question-answer pairs spanning foundational biology, experimental troubleshooting, tool usage, and beyond. We fine-tune an LLM using RL with a rule-based reward signal derived from the synthetic MCQ dataset to enhance domain-specific reasoning. Our results show that reinforcement learning from scientific discussions improves model performance by over 15% compared to the base model on Genome-Bench, narrowing the gap between open-source LLMs and expert-level reasoning. To our knowledge, this is the first end-to-end pipeline for teaching LLMs to reason from scientific discussions, with promising potential for generalization across scientific domains beyond biology.

Building on the success of text-based reasoning models like DeepSeek-R1, extending these capabilities to multimodal reasoning holds great promise. While recent works have attempted to adapt DeepSeek-R1-style reinforcement learning (RL) training paradigms to multimodal large language models (MLLM), focusing on domain-specific tasks like math and visual perception, a critical question remains: How can we achieve the general-purpose visual-language reasoning through RL? To address this challenge, we make three key efforts: (1) A novel Scalable Multimodal QA Synthesis pipeline that autonomously generates context-aware, reasoning-centric question-answer (QA) pairs directly from the given images. (2) The open-source WeThink dataset containing over 120K multimodal QA pairs with annotated reasoning paths, curated from 18 diverse dataset sources and covering various question domains. (3) A comprehensive exploration of RL on our dataset, incorporating a hybrid reward mechanism that combines rule-based verification with model-based assessment to optimize RL training efficiency across various task domains. Across 14 diverse MLLM benchmarks, we demonstrate that our WeThink dataset significantly enhances performance, from mathematical reasoning to diverse general multimodal tasks. Moreover, we show that our automated data pipeline can continuously increase data diversity to further improve model performance.

We propose LLM-Interleaved (LLM-I), a flexible and dynamic framework that reframes interleaved image-text generation as a tool-use problem. LLM-I is designed to overcome the "one-tool" bottleneck of current unified models, which are limited to synthetic imagery and struggle with tasks requiring factual grounding or programmatic precision. Our framework empowers a central LLM or MLLM agent to intelligently orchestrate a diverse toolkit of specialized visual tools, including online image search, diffusion-based generation, code execution, and image editing. The agent is trained to select and apply these tools proficiently via a Reinforcement Learning (RL) framework that features a hybrid reward system combining rule-based logic with judgments from LLM and MLLM evaluators. Trained on a diverse new dataset using four different model backbones, LLM-I demonstrates state-of-the-art performance, outperforming existing methods by a large margin across four benchmarks. We also introduce a novel test-time scaling strategy that provides further performance gains. Project Page: https://github.com/ByteDance-BandAI/LLM-I.

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.

Large language models (LLMs) demonstrate significant reasoning capabilities, particularly through long chain-of-thought (CoT) processes, which can be elicited by reinforcement learning (RL). However, prolonged CoT reasoning presents limitations, primarily verbose outputs due to excessive introspection. The reasoning process in these LLMs often appears to follow a trial-and-error methodology rather than a systematic, logical deduction. In contrast, tree-of-thoughts (ToT) offers a conceptually more advanced approach by modeling reasoning as an exploration within a tree structure. This reasoning structure facilitates the parallel generation and evaluation of multiple reasoning branches, allowing for the active identification, assessment, and pruning of unproductive paths. This process can potentially lead to improved performance and reduced token costs. Building upon the long CoT capability of LLMs, we introduce tree-of-thoughts RL (ToTRL), a novel on-policy RL framework with a rule-based reward. ToTRL is designed to guide LLMs in developing the parallel ToT strategy based on the sequential CoT strategy. Furthermore, we employ LLMs as players in a puzzle game during the ToTRL training process. Solving puzzle games inherently necessitates exploring interdependent choices and managing multiple constraints, which requires the construction and exploration of a thought tree, providing challenging tasks for cultivating the ToT reasoning capability. Our empirical evaluations demonstrate that our ToTQwen3-8B model, trained with our ToTRL, achieves significant improvement in performance and reasoning efficiency on complex reasoning tasks.

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.

Large Language Models (LLMs) demonstrate impressive capabilities but lack robust temporal intelligence, struggling to integrate reasoning about the past with predictions and plausible generations of the future. Meanwhile, existing methods typically target isolated temporal skills, such as question answering about past events or basic forecasting, and exhibit poor generalization, particularly when dealing with events beyond their knowledge cutoff or requiring creative foresight. To address these limitations, we introduce Time-R1, the first framework to endow a moderate-sized (3B-parameter) LLM with comprehensive temporal abilities: understanding, prediction, and creative generation. Our approach features a novel three-stage development path; the first two constitute a reinforcement learning (RL) curriculum driven by a meticulously designed dynamic rule-based reward system. This framework progressively builds (1) foundational temporal understanding and logical event-time mappings from historical data, (2) future event prediction skills for events beyond its knowledge cutoff, and finally (3) enables remarkable generalization to creative future scenario generation without any fine-tuning. Strikingly, experiments demonstrate that Time-R1 outperforms models over 200 times larger, including the state-of-the-art 671B DeepSeek-R1, on highly challenging future event prediction and creative scenario generation benchmarks. This work provides strong evidence that thoughtfully engineered, progressive RL fine-tuning allows smaller, efficient models to achieve superior temporal performance, offering a practical and scalable path towards truly time-aware AI. To foster further research, we also release Time-Bench, a large-scale multi-task temporal reasoning dataset derived from 10 years of news data, and our series of Time-R1 checkpoints.

Rule-based rewards offer a promising strategy for improving reinforcement learning from human feedback (RLHF), but current approaches often rely on manual rule engineering. We present AutoRule, a fully automated method for extracting rules from preference feedback and formulating them into rule-based rewards. AutoRule extraction operates in three stages: it leverages a reasoning model to interpret user preferences, identifies candidate rules from the reasoning chain of these interpretations, and synthesizes them into a unified rule set. Leveraging the finalized rule set, we employ language-model verifiers to compute the fraction of rules satisfied by each output, using this metric as an auxiliary reward alongside the learned reward model during policy optimization. Training a Llama-3-8B model with AutoRule results in a 28.6\% relative improvement in length-controlled win rate on AlpacaEval2.0, and a 6.1\% relative gain in second-turn performance on a held-out MT-Bench subset, compared to a GRPO baseline trained with the same learned reward model but without the rule-based auxiliary reward. Our analysis confirms that the extracted rules exhibit good agreement with dataset preference. We find that AutoRule demonstrates reduced reward hacking compared to a learned reward model when run over two episodes. Finally, our case study suggests that the extracted rules capture unique qualities valued in different datasets. The extracted rules are provided in the appendix, and the code is open-sourced at https://github.com/cxcscmu/AutoRule.

Large language models (LLMs) have demonstrated remarkable performance in reasoning tasks, where reinforcement learning (RL) serves as a key algorithm for enhancing their reasoning capabilities. Currently, there are two mainstream reward paradigms: model-based rewards and rule-based rewards. However, both approaches suffer from limitations: rule-based rewards lack robustness, while model-based rewards are vulnerable to reward hacking. To address these issues, we propose Cooper(Co-optimizing Policy Model and Reward Model), a RL framework that jointly optimizes both the policy model and the reward model. Cooper leverages the high precision of rule-based rewards when identifying correct responses, and dynamically constructs and selects positive-negative sample pairs for continued training the reward model. This design enhances robustness and mitigates the risk of reward hacking. To further support Cooper, we introduce a hybrid annotation strategy that efficiently and accurately generates training data for the reward model. We also propose a reference-based reward modeling paradigm, where the reward model takes a reference answer as input. Based on this design, we train a reward model named VerifyRM, which achieves higher accuracy on VerifyBench compared to other models of the same size. We conduct reinforcement learning using both VerifyRM and Cooper. Our experiments show that Cooper not only alleviates reward hacking but also improves end-to-end RL performance, for instance, achieving a 0.54% gain in average accuracy on Qwen2.5-1.5B-Instruct. Our findings demonstrate that dynamically updating reward model is an effective way to combat reward hacking, providing a reference for better integrating reward models into RL.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (i.e., assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present Router-R1, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.

Reward design in reinforcement learning (RL) is challenging since specifying human notions of desired behavior may be difficult via reward functions or require many expert demonstrations. Can we instead cheaply design rewards using a natural language interface? This paper explores how to simplify reward design by prompting a large language model (LLM) such as GPT-3 as a proxy reward function, where the user provides a textual prompt containing a few examples (few-shot) or a description (zero-shot) of the desired behavior. Our approach leverages this proxy reward function in an RL framework. Specifically, users specify a prompt once at the beginning of training. During training, the LLM evaluates an RL agent's behavior against the desired behavior described by the prompt and outputs a corresponding reward signal. The RL agent then uses this reward to update its behavior. We evaluate whether our approach can train agents aligned with user objectives in the Ultimatum Game, matrix games, and the DealOrNoDeal negotiation task. In all three tasks, we show that RL agents trained with our framework are well-aligned with the user's objectives and outperform RL agents trained with reward functions learned via supervised learning

Recently DeepSeek R1 has shown that reinforcement learning (RL) can substantially improve the reasoning capabilities of Large Language Models (LLMs) through a simple yet effective design. The core of R1 lies in its rule-based reward formulation, which leverages tasks with deterministic ground-truth answers to enable precise and stable reward computation. In the visual domain, we similarly observe that a wide range of visual understanding tasks are inherently equipped with well-defined ground-truth annotations. This property makes them naturally compatible with rule-based reward mechanisms. Motivated by this observation, we investigate the extension of R1-style reinforcement learning to Vision-Language Models (VLMs), aiming to enhance their visual reasoning capabilities. To this end, we develop VLM-R1, a dedicated framework designed to harness RL for improving VLMs' performance on general vision-language tasks. Using this framework, we further explore the feasibility of applying RL to visual domain. Experimental results indicate that the RL-based model not only delivers competitive performance on visual understanding tasks but also surpasses Supervised Fine-Tuning (SFT) in generalization ability. Furthermore, we conduct comprehensive ablation studies that uncover a series of noteworthy insights, including the presence of reward hacking in object detection, the emergence of the "OD aha moment", the impact of training data quality, and the scaling behavior of RL across different model sizes. Through these analyses, we aim to deepen the understanding of how reinforcement learning enhances the capabilities of vision-language models, and we hope our findings and open-source contributions will support continued progress in the vision-language RL community. Our code and model are available at https://github.com/om-ai-lab/VLM-R1

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains -- a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR's empirical success, the fundamental mechanisms governing LLMs' exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs' capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically verifiable outcomes (e.g., correctness or executability) to generate reward signals. While efficient, this framework faces two key limitations: First, its binary feedback is too sparse to capture the quality of the reasoning process. Second, its coarse-grained rewards potentially lead to vanishing gradients. Inspired by observations from human learning, we introduce a RL technique that integrates verifiable outcomes with the model's own confidence estimates. This joint design enriches the reward signal, providing finer-grained feedback and implicitly supervising the reasoning process. Experimental results demonstrate that our proposed method enhances RL performance across multiple datasets and reduces token consumption during inference, while incurring negligible additional training cost. Moreover, it can be used as a plug-in module to enhance other state-of-the-art RL methods.

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

Reward models (RMs) play a critical role in enhancing the reasoning performance of LLMs. For example, they can provide training signals to finetune LLMs during reinforcement learning (RL) and help select the best answer from multiple candidates during inference. In this paper, we provide a systematic introduction to RMs, along with a comprehensive survey of their applications in LLM reasoning. We first review fundamental concepts of RMs, including their architectures, training methodologies, and evaluation techniques. Then, we explore their key applications: (1) guiding generation and selecting optimal outputs during LLM inference, (2) facilitating data synthesis and iterative self-improvement for LLMs, and (3) providing training signals in RL-based finetuning. Finally, we discuss critical open questions regarding the selection, generalization, evaluation, and enhancement of RMs, based on existing research and our own empirical findings. Our analysis aims to provide actionable insights for the effective deployment and advancement of RMs for LLM reasoning.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates promising potential in advancing the reasoning capabilities of LLMs. However, its success remains largely confined to mathematical and code domains. This primary limitation stems from the heavy reliance on domain-specific verifiers, which results in prohibitive complexity and limited scalability. To address the challenge, our key observation is that LLM's intrinsic probability of generating a correct free-form answer directly indicates its own evaluation of the reasoning reward (i.e., how well the reasoning process leads to the correct answer). Building on this insight, we propose RLPR, a simple verifier-free framework that extrapolates RLVR to broader general domains. RLPR uses the LLM's own token probability scores for reference answers as the reward signal and maximizes the expected reward during training. We find that addressing the high variance of this noisy probability reward is crucial to make it work, and propose prob-to-reward and stabilizing methods to ensure a precise and stable reward from LLM intrinsic probabilities. Comprehensive experiments in four general-domain benchmarks and three mathematical benchmarks show that RLPR consistently improves reasoning capabilities in both areas for Gemma, Llama, and Qwen based models. Notably, RLPR outperforms concurrent VeriFree by 7.6 points on TheoremQA and 7.5 points on Minerva, and even surpasses strong verifier-model-dependent approaches General-Reasoner by 1.6 average points across seven benchmarks.

Reinforcement Learning with Human Feedback (RLHF) and Reinforcement Learning with Verifiable Rewards (RLVR) are the main RL paradigms used in LLM post-training, each offering distinct advantages. However, RLHF struggles with interpretability and reward hacking because it relies on human judgments that usually lack explicit criteria, whereas RLVR is limited in scope by its focus on correctness-based verifiers. We propose Reinforcement Learning with Binary Flexible Feedback (RLBFF), which combines the versatility of human-driven preferences with the precision of rule-based verification, enabling reward models to capture nuanced aspects of response quality beyond mere correctness. RLBFF extracts principles that can be answered in a binary fashion (e.g. accuracy of information: yes, or code readability: no) from natural language feedback. Such principles can then be used to ground Reward Model training as an entailment task (response satisfies or does not satisfy an arbitrary principle). We show that Reward Models trained in this manner can outperform Bradley-Terry models when matched for data and achieve top performance on RM-Bench (86.2%) and JudgeBench (81.4%, #1 on leaderboard as of September 24, 2025). Additionally, users can specify principles of interest at inference time to customize the focus of our reward models, in contrast to Bradley-Terry models. Finally, we present a fully open source recipe (including data) to align Qwen3-32B using RLBFF and our Reward Model, to match or exceed the performance of o3-mini and DeepSeek R1 on general alignment benchmarks of MT-Bench, WildBench, and Arena Hard v2 (at <5% of the inference cost).

Reinforcement learning (RL) has been widely adopted in post-training for large language models (LLMs) at scale. Recently, the incentivization of reasoning capabilities in LLMs from RL indicates that proper learning methods could enable effective inference-time scalability. A key challenge of RL is to obtain accurate reward signals for LLMs in various domains beyond verifiable questions or artificial rules. In this work, we investigate how to improve reward modeling (RM) with more inference compute for general queries, i.e. the inference-time scalability of generalist RM, and further, how to improve the effectiveness of performance-compute scaling with proper learning methods. For the RM approach, we adopt pointwise generative reward modeling (GRM) to enable flexibility for different input types and potential for inference-time scaling. For the learning method, we propose Self-Principled Critique Tuning (SPCT) to foster scalable reward generation behaviors in GRMs through online RL, to generate principles adaptively and critiques accurately, resulting in DeepSeek-GRM models. Furthermore, for effective inference-time scaling, we use parallel sampling to expand compute usage, and introduce a meta RM to guide voting process for better scaling performance. Empirically, we show that SPCT significantly improves the quality and scalability of GRMs, outperforming existing methods and models in various RM benchmarks without severe biases, and could achieve better performance compared to training-time scaling. DeepSeek-GRM still meets challenges in some tasks, which we believe can be addressed by future efforts in generalist reward systems. The models will be released and open-sourced.

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning abilities of Large Language Models (LLMs) by using rule-based binary feedback, helping to mitigate reward hacking. However, current RLVR methods typically treat whole responses as single actions, assigning the same reward to every token. This coarse-grained feedback hampers precise credit assignment, making it hard for models to identify which reasoning steps lead to success or failure, and often results in suboptimal policies and inefficient learning. Methods like PPO provide credit assignment through value estimation, but often yield inaccurate and unverifiable signals due to limited sampling. On the other hand, methods using Process Reward Models can provide step-by-step judgments for each reasoning step, but they require high-quality process supervision labels and are time-consuming when applied in online reinforcement learning (RL). To overcome these limitations, we introduce a simple but efficient method Credit Assignment Policy Optimization (CAPO). Given a reasoning response rollout from the policy model, CAPO directly leverages an off-the-shelf, general-purpose LLM as a Generative Process Reward Model (LLM-as-GenPRM) to generate all step-wise critique by one pass, thereby providing verifiable token-level rewards to refine the tokens that were originally assigned identical rule-based rewards. This enables more fine-grained credit assignment in an effective way. Furthermore, to enhance the accuracy and robustness of CAPO, we employ voting mechanisms that scale with the number of generated critiques. Extensive experiments using different backbones like Llama and Qwen models and in different sizes show that CAPO consistently outperforms supervised learning-based and RL-based fine-tuning methods across six challenging mathematical benchmarks and three out-of-domain benchmarks.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing Large Language Models (LLMs), exemplified by the success of OpenAI's o-series. In RLVR, rewards are derived from verifiable signals-such as passing unit tests in code generation or matching correct answers in mathematical reasoning. While effective, this requirement largely confines RLVR to domains with automatically checkable outcomes. To overcome this, we extend the RLVR paradigm to open-ended tasks by integrating rubric-based rewards, where carefully designed rubrics serve as structured, model-interpretable criteria for automatic scoring of subjective outputs. We construct, to our knowledge, the largest rubric reward system to date, with over 10,000 rubrics from humans, LLMs, or a hybrid human-LLM collaboration. Implementing rubric-based RL is challenging; we tackle these issues with a clear framework and present an open-sourced Qwen-30B-A3B model with notable gains: 1) With only 5K+ samples, our system improves by +5.2% on open-ended benchmarks (especially humanities), outperforming a 671B DeepSeek-V3 model by +2.4%, while preserving general and reasoning abilities. 2) Our method provides fine-grained stylistic control, using rubrics as anchors to mitigate the "AI-like" tone and produce more human-like, expressive responses. We share key lessons in rubric construction, data selection, and training, and discuss limitations and future releases.

Reinforcement learning (RL) has been widely used in text generation to alleviate the exposure bias issue or to utilize non-parallel datasets. The reward function plays an important role in making RL training successful. However, previous reward functions are typically task-specific and sparse, restricting the use of RL. In our work, we propose a task-agnostic approach that derives a step-wise reward function directly from a model trained with teacher forcing. We additionally propose a simple modification to stabilize the RL training on non-parallel datasets with our induced reward function. Empirical results show that our method outperforms self-training and reward regression methods on several text generation tasks, confirming the effectiveness of our reward function.

Reinforcement learning (RL) has been widely used in training large language models~(LLMs) for preventing unexpected outputs, \eg reducing harmfulness and errors. However, existing RL methods mostly adopt the instance-level reward, which is unable to provide fine-grained supervision for complex reasoning tasks, and can not focus on the few key tokens that lead to the incorrectness. To address it, we propose a new RL method named RLMEC that incorporates a generative model as the reward model, which is trained by the erroneous solution rewriting task under the minimum editing constraint, and can produce token-level rewards for RL training. Based on the generative reward model, we design the token-level RL objective for training and an imitation-based regularization for stabilizing RL process. And the both objectives focus on the learning of the key tokens for the erroneous solution, reducing the effect of other unimportant tokens. The experiment results on mathematical tasks and question-answering tasks have demonstrated the effectiveness of our approach. Our code and data are available at https://github.com/RUCAIBox/RLMEC.

Outcome-reward reinforcement learning (RL) is a common and increasingly significant way to refine the step-by-step reasoning of multimodal large language models (MLLMs). In the multiple-choice setting - a dominant format for multimodal reasoning benchmarks - the paradigm faces a significant yet often overlooked obstacle: unfaithful trajectories that guess the correct option after a faulty chain of thought receive the same reward as genuine reasoning, which is a flaw that cannot be ignored. We propose Self-Consistency Sampling (SCS) to correct this issue. For each question, SCS (i) introduces small visual perturbations and (ii) performs repeated truncation and resampling of an initial trajectory; agreement among the resulting trajectories yields a differentiable consistency score that down-weights unreliable traces during policy updates. Based on Qwen2.5-VL-7B-Instruct, plugging SCS into RLOO, GRPO, and REINFORCE++ series improves accuracy by up to 7.7 percentage points on six multimodal benchmarks with negligible extra computation. SCS also yields notable gains on both Qwen2.5-VL-3B-Instruct and InternVL3-8B, offering a simple, general remedy for outcome-reward RL in MLLMs.

Generative reward models (also known as LLMs-as-judges), which use large language models (LLMs) to evaluate answer quality, are increasingly adopted in reinforcement learning with verifiable rewards (RLVR). They are often preferred over rigid rule-based metrics, especially for complex reasoning tasks involving free-form outputs. In this paradigm, an LLM is typically prompted to compare a candidate answer against a ground-truth reference and assign a binary reward indicating correctness. Despite the seeming simplicity of this comparison task, we find that generative reward models exhibit surprising vulnerabilities to superficial manipulations: non-word symbols (e.g., ":" or ".") or reasoning openers like "Thought process:" and "Let's solve this problem step by step." can often lead to false positive rewards. We demonstrate that this weakness is widespread across LLMs, datasets, and prompt formats, posing a serious threat for core algorithmic paradigms that rely on generative reward models, such as rejection sampling, preference optimization, and RLVR. To mitigate this issue, we introduce a simple yet effective data augmentation strategy and train a new generative reward model with substantially improved robustness. Our findings highlight the urgent need for more reliable LLM-based evaluation methods. We release our robust, general-domain reward model and its synthetic training data at https://huggingface.co/sarosavo/Master-RM and https://huggingface.co/datasets/sarosavo/Master-RM.

Reward is critical to the evaluation and training of large language models (LLMs). However, existing rule-based or model-based reward methods struggle to generalize to GUI agents, where access to ground-truth trajectories or application databases is often unavailable, and static trajectory-based LLM-as-a-Judge approaches suffer from limited accuracy. To address these challenges, we propose ProRe, a proactive reward system that leverages a general-purpose reasoner and domain-specific evaluator agents (actors). The reasoner schedules targeted state probing tasks, which the evaluator agents then execute by actively interacting with the environment to collect additional observations. This enables the reasoner to assign more accurate and verifiable rewards to GUI agents. Empirical results on over 3K trajectories demonstrate that ProRe improves reward accuracy and F1 score by up to 5.3% and 19.4%, respectively. Furthermore, integrating ProRe with state-of-the-art policy agents yields a success rate improvement of up to 22.4%.

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to real-world tasks often requires balancing objective and subjective evaluation criteria. However, many such tasks lack a single, unambiguous ground truth-making it difficult to define reliable reward signals for post-training language models. While traditional preference-based methods offer a workaround, they rely on opaque reward functions that are difficult to interpret and prone to spurious correlations. We introduce Rubrics as Rewards (RaR), a framework that uses structured, checklist-style rubrics as interpretable reward signals for on-policy training with GRPO. Our best RaR method yields up to a 28% relative improvement on HealthBench-1k compared to simple Likert-based approaches, while matching or surpassing the performance of reward signals derived from expert-written references. By treating rubrics as structured reward signals, we show that RaR enables smaller-scale judge models to better align with human preferences and sustain robust performance across model scales.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have empowered large language models (LLMs) to tackle challenging reasoning tasks such as mathematics and programming. RLVR leverages verifiable outcome rewards to guide policy optimization, enabling LLMs to progressively improve output quality in a grounded and reliable manner. Despite its promise, the RLVR paradigm poses significant challenges, as existing methods often suffer from sparse reward signals and unstable policy gradient updates, particularly in RL-based approaches. To address the challenges, we propose PACS, a novel RLVR framework that achieves imPlicit Actor Critic coupling via a Supervised learning framework. By treating the outcome reward as a predictable label, we reformulate the RLVR problem into a supervised learning task over a score function parameterized by the policy model and optimized using cross-entropy loss. A detailed gradient analysis shows that this supervised formulation inherently recovers the classical policy gradient update while implicitly coupling actor and critic roles, yielding more stable and efficient training. Benchmarking on challenging mathematical reasoning tasks, PACS outperforms strong RLVR baselines, such as PPO and GRPO, achieving superior reasoning performance. For instance, PACS achieves 59.78\% at pass@256 on AIME 2025, representing improvements of 13.32 and 14.36 points over PPO and GRPO. This simple yet powerful framework offers a promising avenue for LLMs post-training with verifiable rewards. Our code and data are available as open source at https://github.com/ritzz-ai/PACS.

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.

Preference-based reinforcement learning (PbRL) is an approach that enables RL agents to learn from preference, which is particularly useful when formulating a reward function is challenging. Existing PbRL methods generally involve a two-step procedure: they first learn a reward model based on given preference data and then employ off-the-shelf reinforcement learning algorithms using the learned reward model. However, obtaining an accurate reward model solely from preference information, especially when the preference is from human teachers, can be difficult. Instead, we propose a PbRL algorithm that directly learns from preference without requiring any reward modeling. To achieve this, we adopt a contrastive learning framework to design a novel policy scoring metric that assigns a high score to policies that align with the given preferences. We apply our algorithm to offline RL tasks with actual human preference labels and show that our algorithm outperforms or is on par with the existing PbRL methods. Notably, on high-dimensional control tasks, our algorithm surpasses offline RL methods that learn with ground-truth reward information. Finally, we show that our algorithm can be successfully applied to fine-tune large language models.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, step-wise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.

Developing custom reasoning models via Reinforcement Learning (RL) that can incorporate organization-specific knowledge has great potential to address problems faced by enterprise customers. In many of these problems, the reward function is verifiable, a setting termed RL with Verifiable Rewards (RLVR). We apply RLVR to a popular data science benchmark called BIRD that measures the ability of an AI agent to convert a natural language query for a database to SQL executions. We apply a simple and general-purpose training recipe involving careful prompt and model selection, a warm-up stage using our offline RL approach called TAO, followed by rigorous online RLVR training. With no additional training data beyond the BIRD training set and no use of proprietary models, our very first submission to the BIRD leaderboard reached state-of-the-art accuracy on the private test set: 73.56% without self-consistency and 75.68% with self-consistency. In the latter case, our model also required fewer generations than the second-best approach. While BIRD is only a proxy task, the simplicity of our framework makes it broadly applicable to enterprise domains such as business intelligence, data science, and coding.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

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.

Reward functions are central in reinforcement learning (RL), guiding agents towards optimal decision-making. The complexity of RL tasks requires meticulously designed reward functions that effectively drive learning while avoiding unintended consequences. Effective reward design aims to provide signals that accelerate the agent's convergence to optimal behavior. Crafting rewards that align with task objectives, foster desired behaviors, and prevent undesirable actions is inherently challenging. This thesis delves into the critical role of reward signals in RL, highlighting their impact on the agent's behavior and learning dynamics and addressing challenges such as delayed, ambiguous, or intricate rewards. In this thesis work, we tackle different aspects of reward shaping. First, we address the problem of designing informative and interpretable reward signals from a teacher's/expert's perspective (teacher-driven). Here, the expert, equipped with the optimal policy and the corresponding value function, designs reward signals that expedite the agent's convergence to optimal behavior. Second, we build on this teacher-driven approach by introducing a novel method for adaptive interpretable reward design. In this scenario, the expert tailors the rewards based on the learner's current policy, ensuring alignment and optimal progression. Third, we propose a meta-learning approach, enabling the agent to self-design its reward signals online without expert input (agent-driven). This self-driven method considers the agent's learning and exploration to establish a self-improving feedback loop.

Reinforcement learning (RL) with verifiable rewards (RLVR) has shown promising results in mathematical reasoning and coding tasks where well-structured reference answers are available. However, its applicability to broader domains remains underexplored. In this work, we study the extension of RLVR to more diverse domains such as medicine, chemistry, psychology, and economics. We observe high agreement in binary judgments across different large language models (LLMs) when objective reference answers exist, which challenges the necessity of large-scale annotation for training domain-specific reward models. To address the limitations of binary rewards when handling unstructured reference answers, we further incorporate model-based soft scoring into RLVR to improve its flexibility. Our experiments show that a distilled generative reward model can serve as an effective cross-domain verifier, providing reliable reward signals for RL without requiring domain-specific annotations. By fine-tuning a base 7B model using various RL algorithms against our reward model, we obtain policies that outperform state-of-the-art open-source aligned LLMs such as Qwen2.5-72B-Instruct and DeepSeek-R1-Distill-Qwen-32B by a large margin, across domains in free-form answer settings. This also strengthens RLVR's robustness and scalability, highlighting its potential for real-world applications with noisy or weak labels.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

Most algorithms in reinforcement learning (RL) require that the objective is formalised with a Markovian reward function. However, it is well-known that certain tasks cannot be expressed by means of an objective in the Markov rewards formalism, motivating the study of alternative objective-specification formalisms in RL such as Linear Temporal Logic and Multi-Objective Reinforcement Learning. To date, there has not yet been any thorough analysis of how these formalisms relate to each other in terms of their expressivity. We fill this gap in the existing literature by providing a comprehensive comparison of 17 salient objective-specification formalisms. We place these formalisms in a preorder based on their expressive power, and present this preorder as a Hasse diagram. We find a variety of limitations for the different formalisms, and argue that no formalism is both dominantly expressive and straightforward to optimise with current techniques. For example, we prove that each of Regularised RL, (Outer) Nonlinear Markov Rewards, Reward Machines, Linear Temporal Logic, and Limit Average Rewards can express a task that the others cannot. The significance of our results is twofold. First, we identify important expressivity limitations to consider when specifying objectives for policy optimization. Second, our results highlight the need for future research which adapts reward learning to work with a greater variety of formalisms, since many existing reward learning methods assume that the desired objective takes a Markovian form. Our work contributes towards a more cohesive understanding of the costs and benefits of different RL objective-specification formalisms.

A broad use case of large language models (LLMs) is in goal-directed decision-making tasks (or "agent" tasks), where an LLM needs to not just generate completions for a given prompt, but rather make intelligent decisions over a multi-turn interaction to accomplish a task (e.g., when interacting with the web, using tools, or providing customer support). Reinforcement learning (RL) provides a general paradigm to address such agent tasks, but current RL methods for LLMs largely focus on optimizing single-turn rewards. By construction, most single-turn RL methods cannot endow LLMs with the ability to intelligently seek information over multiple turns, perform credit assignment, or reason about their past actions -- all of which are critical in agent tasks. This raises the question: how can we design effective and efficient multi-turn RL algorithms for LLMs? In this paper, we develop a framework for building multi-turn RL algorithms for fine-tuning LLMs, that preserves the flexibility of existing single-turn RL methods for LLMs (e.g., proximal policy optimization), while accommodating multiple turns, long horizons, and delayed rewards effectively. To do this, our framework adopts a hierarchical RL approach and runs two RL algorithms in parallel: a high-level off-policy value-based RL algorithm to aggregate reward over utterances, and a low-level RL algorithm that utilizes this high-level value function to train a token policy within each utterance or turn. Our hierarchical framework, Actor-Critic Framework with a Hierarchical Structure (ArCHer), can also give rise to other RL methods. Empirically, we find that ArCHer significantly improves efficiency and performance on agent tasks, attaining a sample efficiency of about 100x over existing methods, while also improving with larger model capacity (upto the 7 billion scale that we tested on).

Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human values. However, RLHF is susceptible to reward hacking, where the agent exploits flaws in the reward function rather than learning the intended behavior, thus degrading alignment. While reward shaping helps stabilize RLHF and partially mitigate reward hacking, a systematic investigation into shaping techniques and their underlying principles remains lacking. To bridge this gap, we present a comprehensive study of the prevalent reward shaping methods. Our analysis suggests three key design principles: (1) RL reward is ideally bounded, (2) RL benefits from rapid initial growth followed by gradual convergence, and (3) RL reward is best formulated as a function of centered reward. Guided by these insights, we propose Preference As Reward (PAR), a novel approach that leverages the latent preferences embedded within the reward model itself as the signal for reinforcement learning. We evaluated PAR on two base models, Gemma2-2B and Llama3-8B, using two datasets, Ultrafeedback-Binarized and HH-RLHF. Experimental results demonstrate PAR's superior performance over other reward shaping methods. On the AlpacaEval 2.0 benchmark, PAR achieves a win rate at least 5 percentage points higher than competing approaches. Furthermore, PAR exhibits remarkable data efficiency, requiring only a single reference reward for optimal performance, and maintains robustness against reward hacking even after two full epochs of training. Code is available at https://github.com/PorUna-byte/PAR.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a promising framework for improving reasoning abilities in Large Language Models (LLMs). However, policy optimized with binary verification prone to overlook potential valuable exploration in reasoning trajectory. In view of heavy annotation cost of golden Process Reward Models (PRMs), recent works attempt using auxiliary signals for reward shaping of process tokens, involving entropy and likelihood collected from logit space. In this work, we offer a novel perspective on shaping RLVR with flow rewards derived from latent space, and propose RLFR, where the flow fields of model latents are constructed from either off-policy high-quality data and on-policy rejection sampling data, and the velocity deviations of policy latents within it are quantified to serve as a reward signal. RLFR first demonstrates that a well-established flow field can be a sound environment for reward signal collection, highlighting the expressive latent space is much underexplored. Moreover, RLFR is able to compress any off-policy expert data as reference for constituting reward signals, and we show that the efficient context dependence compressed within the hidden states are utilized, rather than individual token-level denotation for context comprehending. Experiments on both language and multimodal reasoning benchmarks demonstrate the reliability of flow rewards, and suggesting a promising paradigm for reward shaping with auxiliary signals.

This paper proposes a novel reinforcement learning (RL) framework for credit underwriting that tackles ungeneralizable contextual challenges. We adapt RL principles for credit scoring, incorporating action space renewal and multi-choice actions. Our work demonstrates that the traditional underwriting approach aligns with the RL greedy strategy. We introduce two new RL-based credit underwriting algorithms to enable more informed decision-making. Simulations show these new approaches outperform the traditional method in scenarios where the data aligns with the model. However, complex situations highlight model limitations, emphasizing the importance of powerful machine learning models for optimal performance. Future research directions include exploring more sophisticated models alongside efficient exploration mechanisms.

Text-to-SQL is a challenging task involving multiple reasoning-intensive subtasks, including natural language understanding, database schema comprehension, and precise SQL query formulation. Existing approaches often rely on handcrafted reasoning paths with inductive biases that can limit their overall effectiveness. Motivated by the recent success of reasoning-enhanced models such as DeepSeek R1 and OpenAI o1, which effectively leverage reward-driven self-exploration to enhance reasoning capabilities and generalization, we propose a novel set of partial rewards tailored specifically for the Text-to-SQL task. Our reward set includes schema-linking, AI feedback, n-gram similarity, and syntax check, explicitly designed to address the reward sparsity issue prevalent in reinforcement learning (RL). Leveraging group relative policy optimization (GRPO), our approach explicitly encourages large language models (LLMs) to develop intrinsic reasoning skills necessary for accurate SQL query generation. With models of different sizes, we demonstrate that RL-only training with our proposed rewards consistently achieves higher accuracy and superior generalization compared to supervised fine-tuning (SFT). Remarkably, our RL-trained 14B-parameter model significantly outperforms larger proprietary models, e.g. o3-mini by 4% and Gemini-1.5-Pro-002 by 3% on the BIRD benchmark. These highlight the efficacy of our proposed RL-training framework with partial rewards for enhancing both accuracy and reasoning capabilities in Text-to-SQL tasks.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

Reinforcement learning with verifiable rewards (RLVR) has emerged to be a predominant paradigm for mathematical reasoning tasks, offering stable improvements in reasoning ability. However, Outcome Reward Models (ORMs) in RLVR are too coarse-grained to distinguish flawed reasoning within correct answers or valid reasoning within incorrect answers. This lack of granularity introduces noisy and misleading gradients significantly and hinders further progress in reasoning process quality. While Process Reward Models (PRMs) offer fine-grained guidance for intermediate steps, they frequently suffer from inaccuracies and are susceptible to reward hacking. To resolve this dilemma, we introduce PRocess cOnsistency Filter (PROF), an effective data process curation method that harmonizes noisy, fine-grained process rewards with accurate, coarse-grained outcome rewards. Rather than naively blending PRM and ORM in the objective function (arXiv:archive/2506.18896), PROF leverages their complementary strengths through consistency-driven sample selection. Our approach retains correct responses with higher averaged process values and incorrect responses with lower averaged process values, while maintaining positive/negative training sample balance. Extensive experiments demonstrate that our method not only consistently improves the final accuracy over 4% compared to the blending approaches, but also strengthens the quality of intermediate reasoning steps. Codes and training recipes are available at https://github.com/Chenluye99/PROF.

In recent years, reinforcement learning (RL)-based methods for learning driving policies have gained increasing attention in the autonomous driving community and have achieved remarkable progress in various driving scenarios. However, traditional RL approaches rely on manually engineered rewards, which require extensive human effort and often lack generalizability. To address these limitations, we propose VLM-RL, a unified framework that integrates pre-trained Vision-Language Models (VLMs) with RL to generate reward signals using image observation and natural language goals. The core of VLM-RL is the contrasting language goal (CLG)-as-reward paradigm, which uses positive and negative language goals to generate semantic rewards. We further introduce a hierarchical reward synthesis approach that combines CLG-based semantic rewards with vehicle state information, improving reward stability and offering a more comprehensive reward signal. Additionally, a batch-processing technique is employed to optimize computational efficiency during training. Extensive experiments in the CARLA simulator demonstrate that VLM-RL outperforms state-of-the-art baselines, achieving a 10.5\% reduction in collision rate, a 104.6\% increase in route completion rate, and robust generalization to unseen driving scenarios. Furthermore, VLM-RL can seamlessly integrate almost any standard RL algorithms, potentially revolutionizing the existing RL paradigm that relies on manual reward engineering and enabling continuous performance improvements. The demo video and code can be accessed at: https://zilin-huang.github.io/VLM-RL-website.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow generalized policy iteration that alternates between evaluating the current policy's value and improving the policy based on evaluation. While effective, they often suffer from training instability and diversity collapse, requiring complex heuristic tricks and careful tuning. We observe that standard RLVR in math reasoning can be formalized as a specialized finite-horizon Markov Decision Process with deterministic state transitions, tree-structured dynamics, and binary terminal rewards. Though large in scale, the underlying structure is simpler than general-purpose control settings for which popular RL algorithms (e.g., PPO) were developed, suggesting that several sophisticated techniques in existing methods may be reduced or even omitted. Based on this insight, we prove a surprising result: the optimal action can be recovered from the Q-function of a fixed uniformly random policy, thereby bypassing the generalized policy iteration loop and its associated heuristics. We introduce Random Policy Valuation for Diverse Reasoning (ROVER) to translate this principle into a practical and scalable algorithm for LLM math reasoning, a minimalist yet highly effective RL method that samples actions from a softmax over these uniform-policy Q-values. ROVER preserves diversity throughout training, allowing sustained exploration of multiple valid pathways. Across multiple base models and standard math reasoning benchmarks, ROVER demonstrates superior performance in both quality (+8.2 on pass@1, +16.8 on pass@256) and diversity (+17.6\%), despite its radical simplification compared to strong, complicated existing methods.

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks by using some given positive and negative trajectories for solving the complex task. We assume that the states are represented by first-order predicate logic using which we devise a novel algorithm to identify the subtasks. Then we employ a Large Language Model (LLM) to generate first-order logic rule templates for achieving each subtask. Such rules were then further fined tuned to a rule-based policy via an Inductive Logic Programming (ILP)-based RL agent. Through experiments, we verify the accuracy of our algorithm in detecting subtasks which successfully detect all of the subtasks correctly. We also investigated the quality of the common-sense rules produced by the language model to achieve the subtasks. Our experiments show that our LLM-guided rule template generation can produce rules that are necessary for solving a subtask, which leads to solving complex tasks with fewer assumptions about predefined first-order logic predicates of the environment.

Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach for enhancing such capabilities; however, its ability to foster genuine reasoning remains unclear. We investigate RLVR on two combinatorial problems with fully verifiable solutions: Activity Scheduling and the Longest Increasing Subsequence, using carefully curated datasets with unique optima. Across multiple reward designs, we find that RLVR improves evaluation metrics but often by reinforcing superficial heuristics rather than acquiring new reasoning strategies. These findings highlight the limits of RLVR generalization, emphasizing the importance of benchmarks that disentangle genuine mathematical reasoning from shortcut exploitation and provide faithful measures of progress. Code available at https://github.com/xashru/rlvr-seq-generalization.

Reinforcement learning with verifiable rewards (RLVR) improves language model reasoning by using rule-based rewards in verifiable domains such as mathematics and code. However, RLVR leads to limited generalization for open-ended tasks -- such as writing outline essays or making meal plans -- where humans reason routinely. This paper shows that the RLVR paradigm is effective beyond verifiable domains, and introduces **RL** with **M**odel-rewarded **T**hinking (**RLMT**) for general-purpose chat capabilities. Using diverse real-world prompts, RLMT requires LMs to generate long CoT reasoning before response, and optimizes them with online RL against a preference-based reward model used in RLHF. Across 40 training runs on Llama-3.1-8B and Qwen-2.5-7B (both base and instruct) and multiple optimization algorithms (DPO, PPO, and GRPO), RLMT consistently outperforms standard RLHF pipelines. This includes substantial gains of 3-7 points on three chat benchmarks (AlpacaEval2, WildBench, and ArenaHardV2), along with 1-3 point improvements on other tasks like creative writing and general knowledge. Our best 8B model surpasses GPT-4o in chat and creative writing and rivals Claude-3.7-Sonnet (Thinking). RLMT can also be applied directly to base models without an SFT stage, akin to R1-Zero training. Remarkably, with only 7K prompts, Llama-3.1-8B base trained with our RLMT recipe outperforms Llama-3.1-8B-Instruct post-trained with a complex multi-staged pipeline with 25M+ examples. We close with qualitative and quantitative analyses of how trained models plan their responses. Our results rethink the post-training pipeline and call upon future work to understand and employ thinking more broadly.

Reinforcement learning (RL) often encounters delayed and sparse feedback in real-world applications, even with only episodic rewards. Previous approaches have made some progress in reward redistribution for credit assignment but still face challenges, including training difficulties due to redundancy and ambiguous attributions stemming from overlooking the multifaceted nature of mission performance evaluation. Hopefully, Large Language Model (LLM) encompasses fruitful decision-making knowledge and provides a plausible tool for reward redistribution. Even so, deploying LLM in this case is non-trivial due to the misalignment between linguistic knowledge and the symbolic form requirement, together with inherent randomness and hallucinations in inference. To tackle these issues, we introduce LaRe, a novel LLM-empowered symbolic-based decision-making framework, to improve credit assignment. Key to LaRe is the concept of the Latent Reward, which works as a multi-dimensional performance evaluation, enabling more interpretable goal attainment from various perspectives and facilitating more effective reward redistribution. We examine that semantically generated code from LLM can bridge linguistic knowledge and symbolic latent rewards, as it is executable for symbolic objects. Meanwhile, we design latent reward self-verification to increase the stability and reliability of LLM inference. Theoretically, reward-irrelevant redundancy elimination in the latent reward benefits RL performance from more accurate reward estimation. Extensive experimental results witness that LaRe (i) achieves superior temporal credit assignment to SOTA methods, (ii) excels in allocating contributions among multiple agents, and (iii) outperforms policies trained with ground truth rewards for certain tasks.

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

Program synthesis aims to create accurate, executable code from natural language descriptions. This field has leveraged the power of reinforcement learning (RL) in conjunction with large language models (LLMs), significantly enhancing code generation capabilities. This integration focuses on directly optimizing functional correctness, transcending conventional supervised losses. While current literature predominantly favors policy-based algorithms, attributes of program synthesis suggest a natural compatibility with value-based methods. This stems from rich collection of off-policy programs developed by human programmers, and the straightforward verification of generated programs through automated unit testing (i.e. easily obtainable rewards in RL language). Diverging from the predominant use of policy-based algorithms, our work explores the applicability of value-based approaches, leading to the development of our B-Coder (pronounced Bellman coder). Yet, training value-based methods presents challenges due to the enormous search space inherent to program synthesis. To this end, we propose an initialization protocol for RL agents utilizing pre-trained LMs and a conservative Bellman operator to reduce training complexities. Moreover, we demonstrate how to leverage the learned value functions as a dual strategy to post-process generated programs. Our empirical evaluations demonstrated B-Coder's capability in achieving state-of-the-art performance compared with policy-based methods. Remarkably, this achievement is reached with minimal reward engineering effort, highlighting the effectiveness of value-based RL, independent of reward designs.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key method for improving Large Language Models' reasoning capabilities, yet recent evidence suggests it may paradoxically shrink the reasoning boundary rather than expand it. This paper investigates the shrinkage issue of RLVR by analyzing its learning dynamics and reveals two critical phenomena that explain this failure. First, we expose negative interference in RLVR, where learning to solve certain training problems actively reduces the likelihood of correct solutions for others, leading to the decline of Pass@k performance, or the probability of generating a correct solution within k attempts. Second, we uncover the winner-take-all phenomenon: RLVR disproportionately reinforces problems with high likelihood, correct solutions, under the base model, while suppressing other initially low-likelihood ones. Through extensive theoretical and empirical analysis on multiple mathematical reasoning benchmarks, we show that this effect arises from the inherent on-policy sampling in standard RL objectives, causing the model to converge toward narrow solution strategies. Based on these insights, we propose a simple yet effective data curation algorithm that focuses RLVR learning on low-likelihood problems, achieving notable improvement in Pass@k performance. Our code is available at https://github.com/mail-research/SELF-llm-interference.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in MLLM post-training for perception policy learning. While promising, our initial experiments reveal that incorporating a thinking process through RL does not consistently lead to performance gains across all visual perception tasks. This leads us to delve into the essential role of RL in the context of visual perception. In this work, we return to the fundamentals and explore the effects of RL on different perception tasks. We observe that the perceptual complexity is a major factor in determining the effectiveness of RL. We also observe that reward design plays a crucial role in further approching the upper limit of model perception. To leverage these findings, we propose Perception-R1, a scalable RL framework using GRPO during MLLM post-training. With a standard Qwen2.5-VL-3B-Instruct, Perception-R1 achieves +4.2% on RefCOCO+, +17.9% on PixMo-Count, +4.2% on PageOCR, and notably, 31.9% AP on COCO2017 val for the first time, establishing a strong baseline for perception policy learning.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning capabilities of LLMs, particularly in mathematics and programming tasks. It is widely believed that RLVR enables LLMs to continuously self-improve, thus acquiring novel reasoning abilities that exceed corresponding base models' capacity. In this study, however, we critically re-examines this assumption by measuring the pass@k metric with large values of k to explore the reasoning capability boundary of the models across a wide range of model families and benchmarks. Surprisingly, the RL does not, in fact, elicit fundamentally new reasoning patterns. While RL-trained models outperform their base models at smaller values of k (\eg, k=1), base models can achieve a comparable or even higher pass@k score compared to their RL counterparts at large k values. The reasoning paths generated by RL-trained models are already included in the base models' sampling distribution, suggesting that most reasoning abilities manifested in RL-trained models are already obtained by base models. Further analysis shows that RL training boosts the performance by biasing the model's output distribution toward paths that are more likely to yield rewards, therefore sampling correct responses more efficiently. But this also results in a narrower reasoning capability boundary compared to base models. Similar results are observed in visual reasoning tasks trained with RLVR. Moreover, we find that distillation can genuinely introduce new knowledge into the model, different from RLVR. These findings underscore a critical limitation of RLVR in advancing LLM reasoning abilities which requires us to fundamentally rethink the impact of RL training in reasoning LLMs and the need of a better paradigm. Project Page: https://limit-of-RLVR.github.io

Reinforcement Learning from Verifiable Rewards (RLVR) has been widely adopted as the de facto method for enhancing the reasoning capabilities of large language models and has demonstrated notable success in verifiable domains like math and competitive programming tasks. However, the efficacy of RLVR diminishes significantly when applied to agentic environments. These settings, characterized by multi-step, complex problem solving, lead to high failure rates even for frontier LLMs, as the reward landscape is too sparse for effective model training via conventional RLVR. In this work, we introduce Agent-RLVR, a framework that makes RLVR effective in challenging agentic settings, with an initial focus on software engineering tasks. Inspired by human pedagogy, Agent-RLVR introduces agent guidance, a mechanism that actively steers the agent towards successful trajectories by leveraging diverse informational cues. These cues, ranging from high-level strategic plans to dynamic feedback on the agent's errors and environmental interactions, emulate a teacher's guidance, enabling the agent to navigate difficult solution spaces and promotes active self-improvement via additional environment exploration. In the Agent-RLVR training loop, agents first attempt to solve tasks to produce initial trajectories, which are then validated by unit tests and supplemented with agent guidance. Agents then reattempt with guidance, and the agent policy is updated with RLVR based on the rewards of these guided trajectories. Agent-RLVR elevates the pass@1 performance of Qwen-2.5-72B-Instruct from 9.4% to 22.4% on SWE-Bench Verified. We find that our guidance-augmented RLVR data is additionally useful for test-time reward model training, shown by further boosting pass@1 to 27.8%. Agent-RLVR lays the groundwork for training agents with RLVR in complex, real-world environments where conventional RL methods struggle.

Reward engineering has long been a challenge in Reinforcement Learning (RL) research, as it often requires extensive human effort and iterative processes of trial-and-error to design effective reward functions. In this paper, we propose RL-VLM-F, a method that automatically generates reward functions for agents to learn new tasks, using only a text description of the task goal and the agent's visual observations, by leveraging feedbacks from vision language foundation models (VLMs). The key to our approach is to query these models to give preferences over pairs of the agent's image observations based on the text description of the task goal, and then learn a reward function from the preference labels, rather than directly prompting these models to output a raw reward score, which can be noisy and inconsistent. We demonstrate that RL-VLM-F successfully produces effective rewards and policies across various domains - including classic control, as well as manipulation of rigid, articulated, and deformable objects - without the need for human supervision, outperforming prior methods that use large pretrained models for reward generation under the same assumptions.

The success of many RL techniques heavily relies on human-engineered dense rewards, which typically demand substantial domain expertise and extensive trial and error. In our work, we propose DrS (Dense reward learning from Stages), a novel approach for learning reusable dense rewards for multi-stage tasks in a data-driven manner. By leveraging the stage structures of the task, DrS learns a high-quality dense reward from sparse rewards and demonstrations if given. The learned rewards can be reused in unseen tasks, thus reducing the human effort for reward engineering. Extensive experiments on three physical robot manipulation task families with 1000+ task variants demonstrate that our learned rewards can be reused in unseen tasks, resulting in improved performance and sample efficiency of RL algorithms. The learned rewards even achieve comparable performance to human-engineered rewards on some tasks. See our project page (https://sites.google.com/view/iclr24drs) for more details.

We study what actually works and what doesn't for training large language models as agents via multi-turn reinforcement learning. Despite rapid progress, existing frameworks and definitions are fragmented, and there is no systematic formulation or analysis of which design choices matter across tasks. We address this gap by first breaking down the design space into three inter-related pillars -- environment, reward, and policy -- and empirically derive a recipe for training LLM agents in situated textual domains. In particular, we test TextWorld and ALFWorld, popular domains for testing situated embodied reasoning, as well as SWE-Gym for more software engineering style tasks. (i) For the environment, we analyze the impacts of task complexity in terms of sizes of the state and action spaces as well as optimal solution length, finding that even simple environments within a domain can provide signal on how well an agent can generalize to more complex tasks. (ii) For the reward, we ablate relative reward sparsity, observing that while dense turn-level rewards accelerate training, performance and stability is highly dependent on the choice of RL algorithm. (iii) And for the agent's policy, we explore the interplay between reward sparsity and biased (PPO, GRPO) and unbiased (RLOO) policy gradient methods in addition to showing how to find the optimal Supervised Fine-tuning (SFT) to RL training ratio given a fixed budget. We distill these findings into a training recipe that guides co-design across the three pillars, facilitating research and practical efforts in multi-turn agentic RL. Code: https://github.com/pearls-lab/meow-tea-taro

Reinforcement learning with verifiable rewards (RLVR) has been shown to enhance the reasoning capabilities of large language models (LLMs), enabling the development of large reasoning models (LRMs). However, LRMs such as DeepSeek-R1 and OpenAI o1 often generate verbose responses containing redundant or irrelevant reasoning step-a phenomenon known as overthinking-which substantially increases computational costs. Prior efforts to mitigate this issue commonly incorporate length penalties into the reward function, but we find they frequently suffer from two critical issues: length collapse and training collapse, resulting in sub-optimal performance. To address them, we propose a pipeline for training a Conciseness Reward Model (CRM) that scores the conciseness of reasoning path. Additionally, we introduce a novel reward formulation named Conciseness Reward Function (CRF) with explicit dependency between the outcome reward and conciseness score, thereby fostering both more effective and more efficient reasoning. From a theoretical standpoint, we demonstrate the superiority of the new reward from the perspective of variance reduction and improved convergence properties. Besides, on the practical side, extensive experiments on five mathematical benchmark datasets demonstrate the method's effectiveness and token efficiency, which achieves an 8.1% accuracy improvement and a 19.9% reduction in response token length on Qwen2.5-7B. Furthermore, the method generalizes well to other LLMs including Llama and Mistral. The implementation code and datasets are publicly available for reproduction: https://anonymous.4open.science/r/CRM.

To align conditional text generation model outputs with desired behaviors, there has been an increasing focus on training the model using reinforcement learning (RL) with reward functions learned from human annotations. Under this framework, we identify three common cases where high rewards are incorrectly assigned to undesirable patterns: noise-induced spurious correlation, naturally occurring spurious correlation, and covariate shift. We show that even though learned metrics achieve high performance on the distribution of the data used to train the reward function, the undesirable patterns may be amplified during RL training of the text generation model. While there has been discussion about reward gaming in the RL or safety community, in this discussion piece, we would like to highlight reward gaming in the natural language generation (NLG) community using concrete conditional text generation examples and discuss potential fixes and areas for future work.

Recent advances in reinforcement learning (RL) have significantly improved the complex reasoning capabilities of large language models (LLMs). Despite these successes, existing methods mainly focus on single-domain RL (e.g., mathematics) with verifiable rewards (RLVR), and their reliance on purely online RL frameworks restricts the exploration space, thereby limiting reasoning performance. In this paper, we address these limitations by leveraging rubrics to provide both fine-grained reward signals and offline guidance. We propose RGR-GRPO (Reward and Guidance through Rubrics), a rubric-driven RL framework for multi-domain reasoning. RGR-GRPO enables LLMs to receive dense and informative rewards while exploring a larger solution space during GRPO training. Extensive experiments across 14 benchmarks spanning multiple domains demonstrate that RGR-GRPO consistently outperforms RL methods that rely solely on alternative reward schemes or offline guidance. Compared with verifiable online RL baseline, RGR-GRPO achieves average improvements of +7.0%, +5.4%, +8.4%, and +6.6% on mathematics, physics, chemistry, and general reasoning tasks, respectively. Notably, RGR-GRPO maintains stable entropy fluctuations during off-policy training and achieves superior pass@k performance, reflecting sustained exploration and effective breakthrough beyond existing performance bottlenecks.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

Reinforcement learning for LLM reasoning has rapidly emerged as a prominent research area, marked by a significant surge in related studies on both algorithmic innovations and practical applications. Despite this progress, several critical challenges remain, including the absence of standardized guidelines for employing RL techniques and a fragmented understanding of their underlying mechanisms. Additionally, inconsistent experimental settings, variations in training data, and differences in model initialization have led to conflicting conclusions, obscuring the key characteristics of these techniques and creating confusion among practitioners when selecting appropriate techniques. This paper systematically reviews widely adopted RL techniques through rigorous reproductions and isolated evaluations within a unified open-source framework. We analyze the internal mechanisms, applicable scenarios, and core principles of each technique through fine-grained experiments, including datasets of varying difficulty, model sizes, and architectures. Based on these insights, we present clear guidelines for selecting RL techniques tailored to specific setups, and provide a reliable roadmap for practitioners navigating the RL for the LLM domain. Finally, we reveal that a minimalist combination of two techniques can unlock the learning capability of critic-free policies using vanilla PPO loss. The results demonstrate that our simple combination consistently improves performance, surpassing strategies like GRPO and DAPO.

Recent breakthroughs in large language models (LLMs) have fundamentally shifted recommender systems from discriminative to generative paradigms, where user behavior modeling is achieved by generating target items conditioned on historical interactions. Yet current generative recommenders still suffer from two core limitations: the lack of high-quality negative modeling and the reliance on implicit rewards. Reinforcement learning with verifiable rewards (RLVR) offers a natural solution by enabling on-policy sampling of harder negatives and grounding optimization in explicit reward signals. However, applying RLVR to generative recommenders remains non-trivial. Its unique generation space often leads to invalid or repetitive items that undermine sampling efficiency, and ranking supervision is sparse since most items receive identical zero rewards. To address these challenges, we propose Reinforced Preference Optimization for Recommendation (ReRe), a reinforcement-based paradigm tailored to LLM-based recommenders, an important direction in generative recommendation. ReRe incorporates constrained beam search to improve sampling efficiency and diversify hard negatives, while augmenting rule-based accuracy rewards with auxiliary ranking rewards for finer-grained supervision. Extensive experiments on three real-world datasets demonstrate that ReRe consistently outperforms both traditional and LLM-based recommenders in ranking performance. Further analysis shows that ReRe not only enhances performance across both base and SFT-initialized models but also generalizes robustly across different backbone families and scales. Beyond empirical gains, we systematically investigate the design space of RLVR in recommendation across generation, sampling strategy, reward modeling, and optimization algorithm, offering insights for future research.

Next token prediction is the fundamental principle for training large language models (LLMs), and reinforcement learning (RL) further enhances their reasoning performance. As an effective way to model language, image, video, and other modalities, the use of LLMs for end-to-end extraction of structured visual representations, such as scene graphs, remains underexplored. It requires the model to accurately produce a set of objects and relationship triplets, rather than generating text token by token. To achieve this, we introduce R1-SGG, a multimodal LLM (M-LLM) initially trained via supervised fine-tuning (SFT) on the scene graph dataset and subsequently refined using reinforcement learning to enhance its ability to generate scene graphs in an end-to-end manner. The SFT follows a conventional prompt-response paradigm, while RL requires the design of effective reward signals. Given the structured nature of scene graphs, we design a graph-centric reward function that integrates node-level rewards, edge-level rewards, and a format consistency reward. Our experiments demonstrate that rule-based RL substantially enhances model performance in the SGG task, achieving a zero failure rate--unlike supervised fine-tuning (SFT), which struggles to generalize effectively. Our code is available at https://github.com/gpt4vision/R1-SGG.

Properly defining a reward signal to efficiently train a reinforcement learning (RL) agent is a challenging task. Designing balanced objective functions from which a desired behavior can emerge requires expert knowledge, especially for complex environments. Learning rewards from human feedback or using large language models (LLMs) to directly provide rewards are promising alternatives, allowing non-experts to specify goals for the agent. However, black-box reward models make it difficult to debug the reward. In this work, we propose Object-Centric Assessment with Language Models (OCALM) to derive inherently interpretable reward functions for RL agents from natural language task descriptions. OCALM uses the extensive world-knowledge of LLMs while leveraging the object-centric nature common to many environments to derive reward functions focused on relational concepts, providing RL agents with the ability to derive policies from task descriptions.

Search augmentation empowers Large Language Models with retrieval capabilities to overcome the limitations imposed by static parameters. Recently, Reinforcement Learning leverages tailored reward signals as a viable technique to enhance LLMs performing tasks involving search. However, existing reward modeling for search-augmented LLMs faces several limitations. Rule-based rewards, such as Exact Match, are verifiable but fragile to variations in expression and cannot be applied to long-form workloads. In contrast, generative rewards improve robustness, but designing verifiable and stable rewards for long-form workloads in dynamic corpora remains challenging and also incurs high computational costs. In this paper, we propose a unified and verifiable paradigm, "nugget-as-rubric", which treats atomic information points as structured evaluation criteria for different search-augmentation workloads. Short-form tasks correspond to a single rubric, whereas long-form tasks expand to multiple rubrics aligned with the question's information needs. To support long-form settings, we design an automatic rubric construction pipeline based on query rewriting, which can automatically retrieve passages relevant to each question and extract rubrics from them, both from static corpora and from dynamic online web content. Furthermore, we introduce Search-Gen-V, a 4B-parameter efficient generative verifier under our proposed verifiable paradigm, which is trained via the idea of distillation and a two-stage strategy. Experimental results show that Search-Gen-V achieves strong verification accuracy across different workloads, making it a scalable, robust, and efficient verifiable reward constructor for search-augmented LLMs.

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.

Current Large Language Models (LLMs) often undergo supervised fine-tuning (SFT) to acquire tool use capabilities. However, SFT struggles to generalize to unfamiliar or complex tool use scenarios. Recent advancements in reinforcement learning (RL), particularly with R1-like models, have demonstrated promising reasoning and generalization abilities. Yet, reward design for tool use presents unique challenges: multiple tools may be invoked with diverse parameters, and coarse-grained reward signals, such as answer matching, fail to offer the finegrained feedback required for effective learning. In this work, we present the first comprehensive study on reward design for tool selection and application tasks within the RL paradigm. We systematically explore a wide range of reward strategies, analyzing their types, scales, granularity, and temporal dynamics. Building on these insights, we propose a principled reward design tailored for tool use tasks and apply it to train LLMs using Group Relative Policy Optimization (GRPO). Empirical evaluations across diverse benchmarks demonstrate that our approach yields robust, scalable, and stable training, achieving a 17% improvement over base models and a 15% gain over SFT models. These results highlight the critical role of thoughtful reward design in enhancing the tool use capabilities and generalization performance of LLMs. All the codes are released to facilitate future research.

Reinforcement learning from human feedback (RLHF) offers a promising approach to aligning large language models (LLMs) with human preferences. Typically, a reward model is trained or supplied to act as a proxy for humans in evaluating generated responses during the reinforcement training phase. However, current reward models operate as sequence-to-one models, allocating a single, sparse, and delayed reward to an entire output sequence. This approach may overlook the significant contributions of individual tokens toward the desired outcome. To this end, we propose a more fine-grained, token-level guidance approach for RL training. Specifically, we introduce RED, a novel reward redistribition method that evaluates and assigns specific credit to each token using an off-the-shelf reward model. Utilizing these fine-grained rewards enhances the model's understanding of language nuances, leading to more precise performance improvements. Notably, our method does not require modifying the reward model or introducing additional training steps, thereby incurring minimal computational costs. Experimental results across diverse datasets and tasks demonstrate the superiority of our approach.

Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals. While PbRL has demonstrated practical success in fine-tuning language models, existing theoretical work focuses on regret minimization and fails to capture most of the practical frameworks. In this study, we fill in such a gap between theoretical PbRL and practical algorithms by proposing a theoretical reward-agnostic PbRL framework where exploratory trajectories that enable accurate learning of hidden reward functions are acquired before collecting any human feedback. Theoretical analysis demonstrates that our algorithm requires less human feedback for learning the optimal policy under preference-based models with linear parameterization and unknown transitions, compared to the existing theoretical literature. Specifically, our framework can incorporate linear and low-rank MDPs with efficient sample complexity. Additionally, we investigate reward-agnostic RL with action-based comparison feedback and introduce an efficient querying algorithm tailored to this scenario.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a crucial paradigm for incentivizing reasoning capabilities in Large Language Models (LLMs). Due to vast state-action spaces and reward sparsity in reasoning tasks, existing methods often struggle with deficient exploration and poor sample efficiency. In the paper, we propose DIVER (Diversity-Incentivized Exploration for VersatilE Reasoning), an innovative framework that highlights the pivotal role of global sequence-level diversity to incentivize deep exploration for versatile reasoning. We first conduct a primary empirical study to reveal a strong positive correlation between global diversity and reasoning capacity. Building on this insight, we introduce global diversity incentives as an intrinsic reward to promote deep exploration in a semantically structured space. Incorporating the intrinsic reward, we develop a potential-based reward shaping mechanism to preserve optimal policy invariance and design simple heuristics to mitigate possible reward hacking. Experimental results show that DIVER outperforms competitive RLVR baselines with various exploration strategies on both in-domain and out-of-domain tasks, excelling in both Pass@1 and Pass@k evaluations. Our code is available at https://github.com/NJU-RL/DIVER.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

Large language models (LLMs) are increasingly trained with reinforcement learning (RL) as autonomous agents that reason and act over long horizons in interactive environments. However, sparse and sometimes unverifiable rewards make temporal credit assignment extremely challenging. Recent work attempts to integrate process supervision into agent learning but suffers from biased annotation, reward hacking, high-variance from overly fine-grained signals or failtures when state overlap is rare. We therefore introduce Online Process Reward Learning (OPRL), a general credit-assignment strategy for agentic RL that integrates seamlessly with standard on-policy algorithms without relying on additional rollouts or explicit step labels. In OPRL, we optimize an implicit process reward model (PRM) alternately with the agent's policy to transform trajectory preferences into implicit step rewards through a trajectory-based DPO objective. These step rewards are then used to compute step-level advantages, which are combined with episode-level advantages from outcome rewards for policy update, creating a self-reinforcing loop. Theoretical findings guarantee that the learned step rewards are consistent with trajectory preferences and act as potential-based shaping rewards, providing bounded gradients to stabilize training. Empirically, we evaluate OPRL on three distinct agent benmarks, including WebShop and VisualSokoban, as well as open-ended social interactions with unverfiable rewards in SOTOPIA. Crucially, OPRL shows superior performance over frontier LLMs and strong RL baselines across domains, achieving state-of-the-art results with higher sample-efficiency and lower variance during training. Further analysis also demonstrates the efficient exploration by OPRL using fewer actions, underscoring its potential for agentic learning in real-world scenarios.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a core paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs). To address the lack of verification signals at test time, prior studies incorporate the training of model's self-verification capability into the standard RLVR process, thereby unifying reasoning and verification capabilities within a single LLM. However, previous practice requires the LLM to sequentially generate solutions and self-verifications using two separate prompt templates, which significantly reduces efficiency. In this work, we theoretically reveal that the closed-form solution to the RL objective of self-verification can be reduced to a remarkably simple form: the true reasoning reward of a solution is equal to its last-token self-rewarding score, which is computed as the difference between the policy model's next-token log-probability assigned to any pre-specified token at the solution's last token and a pre-calculated constant, scaled by the KL coefficient. Based on this insight, we propose LaSeR (Reinforcement Learning with Last-Token Self-Rewarding), an algorithm that simply augments the original RLVR loss with a MSE loss that aligns the last-token self-rewarding scores with verifier-based reasoning rewards, jointly optimizing the reasoning and self-rewarding capabilities of LLMs. The optimized self-rewarding scores can be utilized in both training and testing to enhance model performance. Notably, our algorithm derives these scores from the predicted next-token probability distribution of the last token immediately after generation, incurring only the minimal extra cost of one additional token inference. Experiments show that our method not only improves the model's reasoning performance but also equips it with remarkable self-rewarding capability, thereby boosting its inference-time scaling performance.

Large Language Models (LLMs) often struggle with problems that require multi-step reasoning. For small-scale open-source models, Reinforcement Learning with Verifiable Rewards (RLVR) fails when correct solutions are rarely sampled even after many attempts, while Supervised Fine-Tuning (SFT) tends to overfit long demonstrations through rigid token-by-token imitation. To address this gap, we propose Supervised Reinforcement Learning (SRL), a framework that reformulates problem solving as generating a sequence of logical "actions". SRL trains the model to generate an internal reasoning monologue before committing to each action. It provides smoother rewards based on the similarity between the model's actions and expert actions extracted from the SFT dataset in a step-wise manner. This supervision offers richer learning signals even when all rollouts are incorrect, while encouraging flexible reasoning guided by expert demonstrations. As a result, SRL enables small models to learn challenging problems previously unlearnable by SFT or RLVR. Moreover, initializing training with SRL before refining with RLVR yields the strongest overall performance. Beyond reasoning benchmarks, SRL generalizes effectively to agentic software engineering tasks, establishing it as a robust and versatile training framework for reasoning-oriented LLMs.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models (LLMs). In this context, models explore reasoning trajectories and exploit rollouts with correct answers as positive signals for policy optimization. However, these rollouts might involve flawed patterns such as answer-guessing and jump-in-reasoning. Such flawed-positive rollouts are rewarded identically to fully correct ones, causing policy models to internalize these unreliable reasoning patterns. In this work, we first conduct a systematic study of flawed-positive rollouts in RL and find that they enable rapid capability gains during the early optimization stage, while constraining reasoning capability later by reinforcing unreliable patterns. Building on these insights, we propose Flawed-Aware Policy Optimization (FAPO), which presents a parameter-free reward penalty for flawed-positive rollouts, enabling the policy to leverage them as useful shortcuts in the warm-up stage, securing stable early gains, while gradually shifting optimization toward reliable reasoning in the later refinement stage. To accurately and comprehensively detect flawed-positive rollouts, we introduce a generative reward model (GenRM) with a process-level reward that precisely localizes reasoning errors. Experiments show that FAPO is effective in broad domains, improving outcome correctness, process reliability, and training stability without increasing the token budget.

Recent reinforcement learning (RL) approaches have shown strong performance in complex domains such as Atari games, but are often highly sample inefficient. A common approach to reduce interaction time with the environment is to use reward shaping, which involves carefully designing reward functions that provide the agent intermediate rewards for progress towards the goal. However, designing appropriate shaping rewards is known to be difficult as well as time-consuming. In this work, we address this problem by using natural language instructions to perform reward shaping. We propose the LanguagE-Action Reward Network (LEARN), a framework that maps free-form natural language instructions to intermediate rewards based on actions taken by the agent. These intermediate language-based rewards can seamlessly be integrated into any standard reinforcement learning algorithm. We experiment with Montezuma's Revenge from the Atari Learning Environment, a popular benchmark in RL. Our experiments on a diverse set of 15 tasks demonstrate that, for the same number of interactions with the environment, language-based rewards lead to successful completion of the task 60% more often on average, compared to learning without language.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.