Reinforcement Learning with Verifiable Rewards

Also known as RLVR

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Overview

This field studies how to improve language and multimodal models by rewarding outputs whose correctness or task progress can be checked, for example with unit tests, mathematical answers, formal proofs, or simulated environments. Common approaches use policy-gradient methods such as PPO and GRPO, with outcome rewards supplemented by step-level feedback, rollout exploration, or replay to improve credit assignment and data efficiency. Work spans math and coding benchmarks as well as search, GUI, and other interactive agents. A central tension is that rewards must be scalable yet faithful: imperfect or narrow verifiers can be exploited, and a correct final answer does not by itself establish sound reasoning, visual grounding, or robust generalization.

Latest papers

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692 papers137 papers in the last four weeks, up 111% on the four weeks before. 0.8% of all new papers.

Mar 17, 2026

DyJR: Preserving Diversity in Reinforcement Learning with Verifiable Rewards via Dynamic Jensen-Shannon Replay

While Reinforcement Learning (RL) enhances Large Language Model reasoning, on-policy algorithms like GRPO are sample-inefficient as they discard past rollouts. Existing experience replay methods address this by reusing accurate samples for direct policy updates, but this can incur additional storage costs and concentrate the policy on a narrow set of solutions. We argue that historical data should prioritize sustaining local policy plasticity rather than simply reinforcing accuracy. We define local policy plasticity as a persistent ability to remain backtrackable and switchable with respect to recent successful trajectories: throughout training, the policy maintains non-negligible support on recently reachable alternatives, so it can smoothly reallocate probability mass when needed without being locked into a single dominant path. To this end, we propose Dynamic Jensen-Shannon Replay (DyJR), a simple yet effective regularization framework using a dynamic reference distribution from recent trajectories. DyJR introduces two innovations: (1) A Time-Sensitive Dynamic Buffer that uses FIFO and adaptive sizing to retain only temporally proximal samples, synchronizing with model evolution; and (2) Jensen-Shannon Divergence Regularization, which replaces direct replay policy-gradient updates with a regularization signal that discourages premature over-commitment to a single Rank-1 trajectory. Experiments on mathematical reasoning, Text-to-SQL, and coding benchmarks demonstrate that DyJR improves over GRPO as well as baselines such as RLEP and Ex-GRPO, while maintaining training efficiency comparable to the original GRPO. Furthermore, Rank-k token probability evolution and semantic-mode analyses show reduced concentration and greater retention of alternative continuations. Matched admission-objective comparisons and repeated runs provide additional evidence for the roles of DyJR's components.

Long Li, Zhijian Zhou, Tianyi Wang +7

Griffith University, Australia · Fudan University, China · Shanghai Innovation Institute, China +3

Behavioral Diversity in RLReinforcement LearningRL for Language Model ReasoningExperience ReplayReinforcement Learning with Verifiable Rewards
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Mar 17, 2026

Noisy Data is Destructive to Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) has driven recent capability advances of large language models across various domains. Recent studies suggest that improved RLVR algorithms allow models to learn effectively from incorrect annotations, achieving performance comparable to learning from clean data. In this work, we show that these findings are invalid because the claimed 100% noisy training data is "contaminated" with clean data. After rectifying the dataset with a rigorous re-verification pipeline, we demonstrate that noise is destructive to RLVR. We show that existing RLVR algorithm improvements fail to mitigate the impact of noise, achieving similar performance to that of the basic GRPO. Furthermore, we find that the model trained on truly incorrect annotations performs 8-10% worse than the model trained on clean data across mathematical reasoning benchmarks. Finally, we show that these findings hold for real-world noise in Text2SQL tasks, where training on real-world, human annotation errors cause 5-12% lower accuracy than clean data. Our results show that current RLVR methods cannot yet compensate for poor data quality. High-quality data remains essential.

Yuxuan Zhu, Daniel Kang

UIUC · Bridgewater AIA Labs

Reinforcement Learning with Verifiable RewardsNoisy-Label Learning
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Mar 16, 2026

Molecular Identifier Visual Prompt and Verifiable Reinforcement Learning for Chemical Reaction Diagram Parsing

Reaction diagram parsing (RxnDP) is critical for extracting chemical synthesis information from literature. Although recent Vision-Language Models (VLMs) have emerged as a promising paradigm to automate this complex visual reasoning task, their application is fundamentally bottlenecked by the inability to align visual chemical entities with pre-trained knowledge, alongside the inherent discrepancy between token-level training and reaction-level evaluation. To address these dual challenges, this work enhances VLM-based RxnDP from two complementary perspectives: prompting representation and learning paradigms. First, we propose Identifier as Visual Prompting (IdtVP), which leverages naturally occurring molecule identifiers (e.g., bold numerals like 1a) to activate the chemical knowledge acquired during VLM pre-training. IdtVP enables powerful zero-shot and out-of-distribution capabilities, outperforming existing prompting strategies. Second, to further optimize performance within fine-tuning paradigms, we introduce Re3-DAPO, a reinforcement learning algorithm that leverages verifiable rewards to directly optimize reaction-level metrics, thereby achieving consistent gains over standard supervised fine-tuning. Additionally, we release the ScannedRxn benchmark, comprising scanned historical reaction diagrams with real-world artifacts, to rigorously assess model robustness and out-of-distribution ability. Our contributions advance the accuracy and generalization of VLM-based reaction diagram parsing. We will release data, models, and code on GitHub.

Jiahe Song, Chuang Wang, Yinfan Wang +11

Shanghai Jiao Tong University · Shanghai AI Laboratory · Beihang University +2

Visual Prompt LearningReinforcement Learning with Verifiable RewardsRL for VLMs
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Mar 15, 2026

From log⁡π\log π to ππ: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed a leap in Large Language Model (LLM) reasoning, yet its optimization dynamics remain fragile. Standard algorithms like GRPO enforce stability via "hard clipping", which inadvertently stifles exploration by discarding gradients of tokens outside the trust region. While recent "soft clipping" methods attempt to recover these gradients, they suffer from a critical challenge: relying on log-probability gradient (∇θlog⁡πθ\nabla_θ\log π_θ) yields divergent weights as probabilities vanish, destabilizing LLM training. We rethink this convention by establishing probability gradient (∇θπθ\nabla_θπ_θ) as the superior optimization primitive. Accordingly, we propose Decoupled Gradient Policy Optimization (DGPO), which employs a decoupled decay mechanism based on importance sampling ratios. By applying asymmetric, continuous decay to boundary tokens, DGPO resolves the conflict between stability and sustained exploration. Extensive experiments across DeepSeek-R1-Distill-Qwen series models (1.5B/7B/14B) demonstrate that DGPO consistently outperforms strong baselines on various mathematical benchmarks, offering a robust and scalable solution for RLVR. Our code and implementation are available at: https://github.com/FlyTune/DGPO-RL.

Xiaoliang Fu, Jiaye Lin, Yangyi Fang +6

Meituan · Fudan University · Tsinghua University +2

RL for Language Model ReasoningPolicy Gradient MethodsRL Post-TrainingPolicy GradientReinforcement Learning with Verifiable Rewards
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Mar 13, 2026

Rethinking Multiple-Choice Questions for RLVR: Unlocking Potential via Distractor Design

Reinforcement Learning with Verifiable Rewards (RLVR) significantly enhances the reasoning capabilities of Large Language Models. When applied to RLVR, Multiple-Choice Questions (MCQs) offer a scalable source of verifiable data but risk inducing reward hacking, where models shortcut reasoning via random guessing or simple elimination. Current approaches often mitigate this by converting MCQs to open-ended formats, thereby discarding the contrastive signal provided by expert-designed distractors. In this work, we systematically investigate the impact of option design on RLVR. Our analysis highlights two primary insights: (1) Mismatches in option counts between training and testing degrade performance. (2) Strong distractors effectively mitigate random guessing, enabling effective RLVR training even with 2-way questions. Motivated by these findings, we propose Iterative Distractor Curation (IDC), a framework that actively constructs high-quality distractors to block elimination shortcuts and promote deep reasoning. Experiments on various benchmarks demonstrate that our method effectively enhances distractor quality and yields significant gains in RLVR training compared to the original data.

Xu Guo, Qiming Ge, Jian Tong +8

Shanghai AI Laboratory · Shanghai Innovation Institute · Fudan University

RL for Language Model ReasoningMultiple-Choice Question AnsweringReward HackingReinforcement Learning with Verifiable Rewards
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Mar 13, 2026

EvolveCoder: Evolving Test Cases via Adversarial Verification for Code Reinforcement Learning

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for improving code generation in large language models, but its effectiveness is limited by weak and static verification signals in existing coding RL datasets. In this paper, we propose a solution-conditioned and adversarial verification framework that iteratively refines test cases based on the execution behaviors of candidate solutions, with the goal of increasing difficulty, improving discriminative power, and reducing redundancy. Based on this framework, we introduce EvolveCoder-22k, a large-scale coding reinforcement learning dataset constructed through multiple rounds of adversarial test case evolution. Empirical analysis shows that iterative refinement substantially strengthens verification, with pass@1 decreasing from 43.80 to 31.22. Reinforcement learning on EvolveCoder-22k yields stable optimization and consistent performance gains, improving Qwen3-4B by an average of 4.2 points across four downstream benchmarks and outperforming strong 4B-scale baselines. Our results highlight the importance of adversarial, solution-conditioned verification for effective and scalable reinforcement learning in code generation.

Chi Ruan, Dongfu Jiang, Huaye Zeng +2

University of Waterloo · Vector Institute · Harvard University

RL for Code GenerationReinforcement Learning with Verifiable Rewards
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Mar 11, 2026

Hindsight-Anchored Policy Optimization: Learning Through Hindsight with Thompson Sampling-Inspired Adaptive Gating

Reinforcement Learning with Verifiable Rewards improves reasoning in large language models, yet on-policy learning often suffers from cold-start challenges in sparse-reward settings. Recent mixed-policy approaches address this by combining off-policy teacher data with on-policy training. However, simply combining these introduce a persistent off-policy gradient mass that risks training collapse and instability. To address this challenge, we propose Hindsight-Anchored Policy Optimization (HAPO), a framework that allows teacher intervention to act as a temporary support. HAPO employs Beta-Binomial confidence gating, an adaptive gating mechanism that decides when to open the gate for teacher intervention. The intervention operates with Synthetic Success Injection, which replaces the group's lowest-reward rollout with a verified teacher trajectory. We also introduce adaptive threshold annealing, which gradually retracts the support and restores on-policy training within a finite horizon to mitigate persistent off-policy drift. We demonstrate that HAPO can be layered on top of existing mixed-policy methods in a generalizable manner. Across six math reasoning benchmarks and two model scales, HAPO improves the average accuracy of three major mixed-policy methods while maintaining training stability.

Yuning Wu, Ke Wang, Haoran Liu +3

Amazon

Reinforcement LearningRL for Language Model ReasoningReinforcement Learning with Verifiable RewardsSparse-Reward RLOff-Policy RL
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Mar 11, 2026

V0.5V_{0.5}: Generalist Value Model as a Prior for Sparse RL Rollouts

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V0V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V0.5V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V0.5V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

Yi-Kai Zhang, Yueqing Sun, Hongyan Hao +4

School of Artificial Intelligence, Nanjing University · National Key Laboratory for Novel Software Technology, Nanjing University · Meituan, China

Reinforcement Learning with Verifiable RewardsValue Function EstimationPolicy Gradient MethodsSparse-Reward RLAdaptive Sampling
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Mar 11, 2026

Reinforcement Learning with Conditional Expectation Reward

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective in enhancing the reasoning capabilities of large language models, particularly in domains such as mathematics where reliable rule-based verifiers can be constructed. However, the reliance on handcrafted, domain-specific verification rules substantially limits the applicability of RLVR to general reasoning domains with free-form answers, where valid answers often exhibit significant variability, making it difficult to establish complete and accurate rules. To address this limitation, we propose Conditional Expectation Reward (CER), which leverages the large language model itself as an implicit verifier, and is therefore applicable to general domains and eliminates the need for external verifiers or auxiliary models. CER is defined as the expected likelihood of generating the reference answer conditioned on the generated answer. In contrast to rule-based verifiers that yield binary feedback, CER provides a soft, graded reward signal that reflects varying degrees of correctness, making it better suited to tasks where answers vary in correctness. Experimental results demonstrate that CER is effective across a wide range of reasoning tasks, spanning both mathematical and general domains, indicating that CER serves as a flexible and general verification mechanism. The code is available at https://github.com/changyi7231/CER.

Changyi Xiao, Caijun Xu, Yixin Cao

Fudan University

RL for Language Model ReasoningLLM Answer VerificationReinforcement Learning with Verifiable Rewards
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Mar 11, 2026

Does LLM Alignment Really Need Diversity? An Empirical Study of Adapting RLVR Methods for Moral Reasoning

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in logical reasoning tasks, yet whether large language model (LLM) alignment requires fundamentally different approaches remains unclear. Given the apparent tolerance for multiple valid responses in moral reasoning, a natural hypothesis is that alignment tasks inherently require diversity-seeking distribution-matching algorithms rather than reward-maximizing policy-based methods. We conduct the first comprehensive empirical study comparing both paradigms on MoReBench. To enable stable RLVR training, we build a rubric-grounded reward pipeline by training a Qwen3-1.7B judge model. Contrary to our hypothesis, we find that distribution-matching approaches do not demonstrate significant advantages over reward-maximizing methods as expected on alignment tasks. Through semantic visualization mapping high-reward responses to semantic space, we demonstrate that moral reasoning exhibits more concentrated high-reward distributions than mathematical reasoning, where diverse solution strategies yield similarly high rewards. This counter-intuitive finding explains why mode-seeking optimization proves equally or more effective for alignment tasks. Our results suggest that alignment tasks do not inherently require diversity-preserving algorithms, and standard reward-maximizing RLVR methods can effectively transfer to moral reasoning without explicit diversity mechanisms.

Zhaowei Zhang, Xiaohan Liu, Xuekai Zhu +6

Institute for Artificial Intelligence, Peking University · University of Michigan · Shanghai Jiao Tong University +3

LLM AlignmentDistribution MatchingReinforcement Learning with Verifiable RewardsMoral Reasoning in Language Models
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Mar 11, 2026

Safe and Scalable Web Agent Learning via Recreated Websites

Training autonomous web agents is fundamentally limited by the environments they learn from: real-world websites are unsafe to explore, hard to reset, and rarely provide verifiable feedback. We propose VeriEnv, a framework that treats language models as environment creators, automatically cloning real-world websites into fully executable, verifiable synthetic environments. By exposing controlled internal access via a Python SDK, VeriEnv enables agents to self-generate tasks with deterministic, programmatically verifiable rewards, eliminating reliance on heuristic or LLM-based judges. This design decouples agent learning from unsafe real-world interaction while enabling scalable self-evolution through environment expansion. Through experiments on web agent benchmarks, we show that agents trained with VeriEnv generalize to unseen websites, achieve site-specific mastery through self-evolving training, and benefit from scaling the number of training environments. Code and resources will be released at https://github.com/kyle8581/VeriEnv upon acceptance.

Hyungjoo Chae, Jungsoo Park, Alan Ritter

School of Interactive Computing, Georgia Institute of Technology

Web AgentsLLM Agent TrainingReinforcement Learning with Verifiable RewardsSelf-Evolving Agents
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Mar 10, 2026

CLIPO: Contrastive Learning in Policy Optimization Generalizes RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capacity of Large Language Models (LLMs). However, RLVR solely relies on final answers as outcome rewards, neglecting the correctness of intermediate reasoning steps. Training on these process-wrong but outcome-correct rollouts can lead to hallucination and answer-copying, severely undermining the model's generalization and robustness. To address this, we incorporate a Contrastive Learning mechanism into the Policy Optimization (CLIPO) to generalize the RLVR process. By optimizing a contrastive loss over successful rollouts, CLIPO steers the LLM to capture the invariant structure shared across correct reasoning paths. This provides a more robust cross-trajectory regularization than the original single-path supervision in RLVR, effectively mitigating step-level reasoning inconsistencies and suppressing hallucinatory artifacts. In experiments, CLIPO consistently improves multiple RLVR baselines across diverse reasoning benchmarks, demonstrating uniform improvements in generalization and robustness for policy optimization of LLMs. Our code and training recipes are available at https://github.com/Qwen-Applications/CLIPO.

Sijia Cui, Pengyu Cheng, Jiajun Song +6

Qwen Large Model Application Team, Alibaba · Institute of Automation, Chinese Academy of Sciences

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsReasoning Consistency in Language ModelsContrastive RL
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Mar 10, 2026

Good Reasoning Makes Good Demonstrations: Implicit Reasoning Quality Supervision via In-Context Reinforcement Learning

Reinforcement Learning with Verifiable Rewards (RLVR) improves reasoning in large language models but treats all correct solutions equally, potentially reinforcing flawed traces that arrive at correct answers by chance. We observe that better reasoning makes better demonstrations: high-quality solutions serve as more effective in-context examples than low-quality ones. We term this teaching ability Demonstration Utility, and show that the policy model's own in-context learning ability provides an efficient way to measure it, yielding a quality signal termed Evidence Gain. To leverage this signal during training, we introduce In-Context RLVR, which prepends demonstrations before each rollout. Theoretically, we prove that this simple input modification implicitly reweights rewards by a factor approximately proportional to Evidence Gain, assigning higher weights to high-quality traces without requiring costly computation. Experiments on mathematical reasoning benchmarks demonstrate consistent improvements in both accuracy and reasoning quality over standard RLVR baselines. Our codes and datasets are available at https://github.com/Mithas-114/IC-DAPO.

Tiehua Mei, Minxuan Lv, Leiyu Pan +5

School of Data Science, Fudan University · University of Chinese Academy of Sciences · College of Intelligence and Computing, Tianjin University

RL for Language Model ReasoningLLM ReasoningIn-Context RLReinforcement Learning with Verifiable RewardsReasoning Evaluation
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Mar 10, 2026

Decoupling Reasoning and Confidence: Resurrecting Calibration in Reinforcement Learning from Verifiable Rewards

Reinforcement Learning from Verifiable Rewards (RLVR) significantly enhances large language models (LLMs) reasoning but severely suffers from calibration degeneration, where models become excessively over-confident in incorrect answers. Previous studies devote to directly incorporating calibration objective into existing optimization target. However, our theoretical analysis demonstrates that there exists a fundamental gradient conflict between the optimization for maximizing policy accuracy and minimizing calibration error. Building on this insight, we propose DCPO, a simple yet effective framework that systematically decouples reasoning and calibration objectives. Extensive experiments demonstrate that our DCPO not only preserves accuracy on par with GRPO but also achieves the best calibration performance and substantially mitigates the over-confidence issue. Our study provides valuable insights and practical solution for more reliable LLM deployment.

Zhengzhao Ma, Xueru Wen, Boxi Cao +6

Chinese Information Processing Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China +2

Reinforcement LearningRL for Language Model ReasoningLanguage Model CalibrationReinforcement Learning with Verifiable Rewards
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Mar 9, 2026

How Far Can Unsupervised RLVR Scale LLM Training?

Unsupervised reinforcement learning with verifiable rewards (URLVR) offers a pathway to scale LLM training beyond the supervision bottleneck by deriving rewards without ground truth labels. Recent works leverage model intrinsic signals, showing promising early gains, yet their potential and limitations remain unclear. In this work, we revisit URLVR and provide a comprehensive analysis spanning taxonomy, theory and extensive experiments. We first classify URLVR methods into intrinsic versus external based on reward sources, then establish a unified theoretical framework revealing that all intrinsic methods converge toward sharpening the model's initial distribution This sharpening mechanism succeeds when initial confidence aligns with correctness but fails catastrophically when misaligned. Through systematic experiments, we show intrinsic rewards consistently follow a rise-then-fall pattern across methods, with collapse timing determined by model prior rather than engineering choices. Despite these scaling limits, we find intrinsic rewards remain valuable in test-time training on small datasets, and propose Model Collapse Step to measure model prior, serving as a practical indicator for RL trainability. Finally, we explore external reward methods that ground verification in computational asymmetries, showing preliminary evidence they may escape the confidence-correctness ceiling. Our findings chart boundaries for intrinsic URLVR while motivating paths toward scalable alternatives.

Bingxiang He, Yuxin Zuo, Zeyuan Liu +18

Tsinghua University · Shanghai AI Lab · Xi’an Jiaotong University +3

RL for Language ModelsReinforcement Learning with Verifiable RewardsIntrinsic Reward Methods
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Mar 9, 2026

SWE-Fuse: Empowering Software Agents via Issue-free Trajectory Learning and Entropy-aware RLVR Training

Large language models (LLMs) have transformed the software engineering landscape. Recently, numerous LLM-based agents have been developed to address real-world software issue fixing tasks. Despite their state-of-the-art performance, Despite achieving state-of-the-art performance, these agents face a significant challenge: Insufficient high-quality issue descriptions. Real-world datasets often exhibit misalignments between issue descriptions and their corresponding solutions, introducing noise and ambiguity that mislead automated agents and limit their problem-solving effectiveness. We propose SWE-Fuse, an issue-description-aware training framework that fuses issue-description-guided and issue-free samples for training SWE agents. It consists of two key modules: (1) An issue-free-driven trajectory learning module for mitigating potentially misleading issue descriptions while enabling the model to learn step-by-step debugging processes; and (2) An entropy-aware RLVR training module, which adaptively adjusts training dynamics through entropy-driven clipping. It applies relaxed clipping under high entropy to encourage exploration, and stricter clipping under low entropy to ensure training stability. We evaluate SWE-Fuse on the widely studied SWE-bench Verified benchmark shows to demonstrate its effectiveness in solving real-world software problems. Specifically, SWE-Fuse outperforms the best 8B and 32B baselines by 43.0% and 60.2% in solve rate, respectively. Furthermore, integrating SWE-Fuse with test-time scaling (TTS) enables further performance improvements, achieving solve rates of 49.8% and 65.2% under TTS@8 for the 8B and 32B models, respectively.

Xin-Cheng Wen, Binbin Chen, Haoxuan Lan +3

Ant Group · The Chinese University of Hong Kong

Software Engineering AgentsLLM Agent TrainingAutomated Program RepairRL for Code GenerationReinforcement Learning with Verifiable Rewards
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Mar 7, 2026

Countdown-Code: A Testbed for Studying The Emergence and Generalization of Reward Hacking in RLVR

Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often expensive or impossible to compute. We introduce Countdown-Code, a minimal environment where models can both solve a mathematical reasoning task and manipulate the test harness. This dual-access design creates a clean separation between proxy rewards (test pass/fail) and true rewards (mathematical correctness), enabling accurate measurement of reward-hacking rates. Using this environment, we study reward hacking in open-weight LLMs and find that such behaviors can be unintentionally learned during supervised fine-tuning (SFT) when even a small fraction of reward-hacking trajectories leak into training data. As little as 1% contamination in distillation SFT data is sufficient for models to internalize reward hacking which resurfaces during subsequent reinforcement learning (RL). We further show that RL amplifies misalignment and drives its generalization beyond the original domain. We open-source our environment and code to facilitate future research on reward hacking in LLMs. Our results reveal a previously underexplored pathway through which reward hacking can emerge and persist in LLMs, underscoring the need for more rigorous validation of synthetic SFT data. Code is available at https://github.com/zohaib-khan5040/Countdown-Code.

Muhammad Khalifa, Zohaib Khan, Omer Tafveez +2

NVIDIA · University of Michigan · University of Illinois Urbana-Champaign

RL BenchmarksReward HackingRL for Language Model ReasoningReinforcement Learning with Verifiable Rewards
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Mar 7, 2026

Chart-RL: Generalized Chart Comprehension via Reinforcement Learning with Verifiable Rewards

Accurate chart comprehension represents a critical challenge in advancing multimodal learning systems, as extensive information is compressed into structured visual representations. However, existing vision-language models (VLMs) frequently struggle to generalize on unseen charts because it requires abstract, symbolic, and quantitative reasoning over structured visual representations. In this work, we introduce Chart-RL, an effective reinforcement learning (RL) method that employs mathematically verifiable rewards to enhance chart question answering in VLMs. Our experiments demonstrate that Chart-RL consistently outperforms supervised fine-tuning (SFT) across different chart understanding benchmarks, achieving relative improvements of 16.7% on MutlChartQA, and 11.5% on ChartInsights. We conduct robustness analysis, where Chart-RL achieves enhanced performance in 18 of 25 perturbed chart categories, demonstrating strong consistency and reasoning capability across visual variations. Furthermore, we demonstrate that task difficulty and inherent complexity are more critical than data quantity in RL training. For instance, Chart-RL trained on merely 10 complex chart-query examples significantly outperforms models trained on over 6,000 simple examples. Additionally, training on challenging reasoning tasks not only improves in-domain generalization relative to simpler tasks, but also facilitate strong transfer to out-of-domain visual mathematical problems.

Xin Zhang, Xingyu Li, Rongguang Wang +4

Oracle AI

Chart QARL for VLMsReinforcement Learning with Verifiable RewardsVLM Robustness
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Mar 6, 2026

Reference-guided Policy Optimization for Molecular Optimization via LLM Reasoning

Large language models (LLMs) benefit substantially from supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR) in reasoning tasks. However, these recipes perform poorly in instruction-based molecular optimization, where each data point typically provides only a single optimized reference molecule and no step-by-step optimization trajectory. We reveal that answer-only SFT on the reference molecules collapses reasoning, and RLVR provides sparse feedback under similarity constraints due to the model's lack of effective exploration, which slows learning and limits optimization. To encourage the exploration of new molecules while balancing the exploitation of the reference molecules, we introduce Reference-guided Policy Optimization (RePO), an optimization approach that learns from reference molecules without requiring trajectory data. At each update, RePO samples candidate molecules with their intermediate reasoning trajectories from the model and trains the model using verifiable rewards that measure property satisfaction under similarity constraints in an RL manner. Meanwhile, it applies reference guidance by keeping the policy's intermediate reasoning trajectory as context and training only the answer in a supervised manner. Together, the RL term promotes exploration, while the guidance term mitigates reward sparsity and stabilizes training by grounding outputs to references when many valid molecular edits exist. Across molecular optimization benchmarks, RePO consistently outperforms SFT and RLVR baselines (e.g., GRPO), achieving improvements on the optimization metric (Success Rate ×\times Similarity), improving balance across competing objectives, and generalizing better to unseen instruction styles. Our code is publicly available at https://github.com/tmlr-group/RePO.

Xuan Li, Zhanke Zhou, Zongze Li +4

Hong Kong Baptist University · CMIC, Shanghai Jiao Tong University · DAMO Academy, Alibaba Group +1

Molecular OptimizationLarge Language Model-Guided OptimizationPolicy OptimizationRL for Language ModelsReinforcement Learning with Verifiable Rewards
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Mar 4, 2026

BeamPERL: Parameter-Efficient RL with Verifiable Rewards Specializes Compact LLMs for Structured Beam Mechanics Reasoning

Can reinforcement learning with hard, verifiable rewards teach a compact language model to reason about physics, or does it primarily learn to pattern-match toward correct answers? We study this question by training a 1.5B-parameter reasoning model on beam statics, a classic engineering problem, using parameter-efficient RLVR with binary correctness rewards from symbolic solvers, without teacher-generated reasoning traces. The best BeamPERL checkpoint achieves a 66.7% improvement in Pass@1 over the base model. However, the learned competence is anisotropic: the model generalizes compositionally (more loads) but fails under topological shifts (moved supports) that require the same equilibrium equations. Intermediate checkpoints yield the strongest reasoning, while continued optimization degrades robustness while maintaining reward. These findings reveal a key limitation of outcome-level alignment: reinforcement learning with exact physics rewards induces procedural solution templates rather than internalization of governing equations. The precision of the reward signal - even when analytically exact - does not by itself guarantee transferable physical reasoning. Our results suggest that verifiable rewards may need to be paired with structured reasoning scaffolding to move beyond template matching toward robust scientific reasoning.

Tarjei Paule Hage, Markus J. Buehler

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA · Department of Civil and Environmental Engineering, Department of Mechanical Engineering, Schwarzman College of Computing, Massachusetts Institute of Technology, Cambridge, MA, USA

Structural EngineeringRL for Language Model ReasoningScientific Reasoning in Language ModelsReinforcement Learning with Verifiable RewardsReinforcement LearningLanguage Model Robustness
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Mar 3, 2026

Heterogeneous Agent Collaborative Reinforcement Learning

We introduce Heterogeneous Agent Collaborative Reinforcement Learning (HACRL), a new Reinforcement Learning from Verifiable Reward (RLVR) problem that addresses the inefficiencies of isolated multi-agent on-policy optimization. HACRL enables collaborative optimization with independent execution: heterogeneous agents share verified rollouts during training to mutually improve, while operating independently at inference time. Unlike LLM-based multi-agent reinforcement learning (MARL), HACRL does not require coordinated deployment, and unlike on-/off-policy distillation, it enables bidirectional mutual learning among heterogeneous agents rather than one-directional homogeneous teacher-to-student transfer. Building on this problem, we propose HACPO, a collaborative RL algorithm that enables principled rollout sharing to maximize sample utilization and cross-agent knowledge transfer. To mitigate capability discrepancies and policy distribution shifts, HACPO introduces four tailored mechanisms with theoretical guarantees on unbiased advantage estimation. Extensive experiments across diverse heterogeneous model combinations and reasoning benchmarks show that HACPO consistently improves all participating agents, outperforming GSPO with double rollouts by an average of 3.6% while using only half the rollout cost.

Zhixia Zhang, Zixuan Huang, Gongxun Li +10

Beihang University · Bytedance China · Apple +2

Multi-Agent CollaborationHeterogeneous MARLCooperative MARLReinforcement Learning with Verifiable Rewards
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Mar 2, 2026

Tool Verification for Test-Time Reinforcement Learning

Test-time reinforcement learning (TTRL) has emerged as a promising paradigm for Recursive Self-Improving AI (RSI) by adapting Large Reasoning Models (LRMs) on unlabeled test inputs, using self-consensus rewards derived from majority voting over sampled rollouts. However, majority voting can mistake popularity for correctness: a spurious yet high-frequency unverified consensus may become a biased reward signal, causing test-time RL to reinforce frequent but wrong answers and collapse into an incorrect mode. We address this false-popular failure mode with T3^3RL (Tool-Verification for Test-Time Reinforcement Learning), a verification-aware test-time RL framework. T3^3RL grounds pseudo-label construction in external tool evidence. Concretely, a verifier utilizes external tool evidence (e.g., from code execution) to upweight verified rollouts during a verification-aware voting, producing more reliable pseudo-labels for training. Across various math difficulties (MATH-500, AMC, and AIME 2024) and diverse backbone families, T3^3RL significantly improves over TTRL, with better performance on harder problems. T3^3RL is positioned as a verified online data synthesizer, highlighting the role of tool verification in reliable online adaptation. T3^3RL is extensible to verifiable domains and provides training and inference efficiency.

Ruotong Liao, Nikolai Röhrich, Xiaohan Wang +4

Ludwig-Maximilians University of Munich · MCML · Stanford University

Test-Time RLRL for Language Model ReasoningReinforcement Learning with Verifiable Rewards
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Mar 2, 2026

LongRLVR: Long-Context Reinforcement Learning Requires Verifiable Context Rewards

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capabilities of Large Language Models (LLMs) by optimizing them against factual outcomes. However, this paradigm falters in long-context scenarios, as its reliance on internal parametric knowledge is ill-suited for tasks requiring contextual grounding--the ability to find and reason over externally provided information. We identify a key reason for this failure: a reward based solely on the final answer is too sparse to effectively guide the model for identifying relevant evidence. We formally prove that the outcome-only reward leads to significant vanishing gradients for the context grounding process, rendering learning intractable. To overcome this bottleneck, we introduce LongRLVR to augment the sparse answer reward with a dense and verifiable context reward. This auxiliary signal directly incentivizes the model for selecting the correct grounding information, providing a robust learning gradient that solves the underlying optimization challenge. We validate our method on challenging long-context benchmarks using Qwen and LLaMA models. LongRLVR consistently and significantly outperforms the standard RLVR across all models and benchmarks, e.g., boosting a 14B model's scores on RULER-QA from 73.17 to 88.90 and on LongBench v2 from 39.8 to 46.5. Our work demonstrates that explicitly rewarding the grounding process is a critical and effective strategy for unlocking the full reasoning potential of LLMs in long-context applications. Our code is available at https://github.com/real-absolute-AI/LongRLVR.

Guanzheng Chen, Michael Qizhe Shieh, Lidong Bing

National University of Singapore · MiroMind AI · absolute AI

RL for Language ModelsReinforcement Learning with Verifiable RewardsLLM GroundingReward ShapingLong-Context Language Model Evaluation
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Mar 2, 2026

Efficient RLVR Training via Weighted Mutual Information Data Selection

Reinforcement learning (RL) plays a central role in improving the reasoning and alignment of large language models, yet its efficiency critically depends on how training data are selected. Existing online selection strategies predominantly rely on difficulty-based heuristics, favouring datapoints with intermediate success rates, implicitly equating difficulty with informativeness and neglecting epistemic uncertainty arising from limited evidence. We introduce InSight, an INformation-guided data SamplInG metHod for RL Training, grounded in a weighted mutual information objective. By modeling data outcomes with Bayesian latent success rates, we show that expected uncertainty reduction decomposes into complementary difficulty- and evidence-dependent components, revealing a fundamental limitation of difficulty-only selection. Leveraging this observation, InSight constructs a stable acquisition score based on the mean belief of datapoints' success rather than noisy sampled outcomes, and naturally extends to multi-rollout settings common in reinforcement learning with verifiable rewards (RLVR). Extensive experiments demonstrate that InSight consistently achieves state-of-the-art performance and improves training efficiency, including a +1.41 average gain on Planning & Mathmatics benchmarks, +1.01 improvement on general reasoning, and up to ~2.2x acceleration, with negligible additional computational overhead.

Xinyu Zhou, Boyu Zhu, Haotian Zhang +2

HKUST(GZ) · UCL · Kuaishou Technology +1

Reinforcement LearningRL for Language Model ReasoningSample-Efficient RLReinforcement Learning with Verifiable Rewards
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Mar 2, 2026

Efficient Token-Level Policy Optimization for Masked Diffusion Models via Velocity Alignment

Reinforcement Learning with Verifiable Rewards (RLVR) successfully aligns autoregressive models in rigorous domains like mathematical reasoning and code generation. However, applying RLVR to Diffusion Large Language Models (dLLMs) is hindered by intractable sequence-level likelihoods, forcing existing methods to rely on unstable, high-variance approximations. We propose Sequence Likelihood-Free Policy Optimization (LFPO), an efficient framework that circumvents this bottleneck by formulating policy alignment as discrete velocity alignment. Inspired by continuous flow matching, LFPO eschews trajectory-level estimation and directly optimizes denoising logits via contrastive token-level updates, providing a stable, low-variance surrogate. Furthermore, predicting terminal solutions from intermediate states implicitly straightens the generation trajectory, enabling high-quality sampling with significantly fewer denoising iterations. Extensive experiments on reasoning and coding benchmarks demonstrate that LFPO matches or exceeds the accuracy of likelihood-based baselines while substantially accelerating inference.

Chenxing Wei, Jiazhen Kang, Hong Wang +8

Shenzhen University, China · Guangming Laboratory, China · ByteDance, China +5

RL for Diffusion ModelsPolicy OptimizationDiffusion Language Model InferenceMasked Diffusion ModelsReinforcement Learning with Verifiable RewardsDiffusion Model Inference Acceleration
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Feb 28, 2026

RLAR: An Agentic Reward System for Multi-task Reinforcement Learning on Large Language Models

Large language model alignment via reinforcement learning depends critically on reward function quality. However, static, domain-specific reward models are often costly to train and exhibit poor generalization in out-of-distribution scenarios encountered during RL iterations. We present RLAR (Reinforcement Learning from Agent Rewards), an agent-driven framework that dynamically assigns tailored reward functions to individual queries. Specifically, RLAR transforms reward acquisition into a dynamic tool synthesis and invocation task. It leverages LLM agents to autonomously retrieve optimal reward models from the Internet and synthesize programmatic verifiers through code generation. This allows the reward system to self-evolve with the shifting data distributions during training. Experimental results demonstrate that RLAR yields consistent performance gains ranging from 10 to 60 across mathematics, coding, translation, and dialogue tasks. On RewardBench-V2, RLAR significantly outperforms static baselines and approaches the performance upper bound, demonstrating superior generalization through dynamic reward orchestration. The data and code are available on this link: https://github.com/ZhuoerFeng/RLAR.

Andrew Zhuoer Feng, Cunxiang Wang, Bosi Wen +4

Tsinghua Univeristy · Peking University

RL for Language ModelsReward Design for RLReward ModelingReinforcement Learning with Verifiable RewardsMulti-Task RLAgentic RL
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Feb 27, 2026

Recycling Failures: Salvaging Exploration in RLVR via Fine-Grained Off-Policy Guidance

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

Yanwei Ren, Haotian Zhang, Likang Xiao +6

School of Artificial Intelligence, Beihang University, Beijing, China · Hangzhou International Innovation Institute, Beihang University, Hangzhou, China · The Hong Kong Polytechnic University, Hong Kong SAR, China +3

RL for Language Model ReasoningReinforcement Learning with Verifiable RewardsOff-Policy RL
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Feb 26, 2026

Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning

Large reasoning models (LRMs) have emerged as a powerful paradigm for solving complex real-world tasks. In practice, these models are predominantly trained via Reinforcement Learning with Verifiable Rewards (RLVR), yet most existing outcome-only RLVR pipelines rely almost exclusively on a binary correctness signal and largely ignore the model's intrinsic uncertainty. We term this discrepancy the uncertainty-reward mismatch, under which high- and low-uncertainty solutions are treated equivalently, preventing the policy from "Know What You Know" and impeding the shift from optimizing for correct answers to optimizing effective reasoning paths. This limitation is especially critical in reasoning-centric tasks such as mathematics and question answering, where performance hinges on the quality of the model's internal reasoning process rather than mere memorization of final answers. To address this, we propose EGPO, a metacognitive entropy calibration framework that explicitly integrates intrinsic uncertainty into RLVR for enhancing LRMs. EGPO estimates per-sample uncertainty using a zero-overhead entropy proxy derived from token-level likelihoods and aligns it with extrinsic correctness through an asymmetric calibration mechanism that preserves correct reasoning while selectively regulating overconfident failures, thereby enabling stable and uncertainty-aware policy optimization. Moreover, EGPO recovers informative learning signals from otherwise degenerate group-based rollouts without modifying the verifier or reward definition. Extensive experiments across multiple benchmarks demonstrate that the proposed EGPO leads to substantial and consistent improvements in reasoning performance, establishing a principled path for advancing LRMs through metacognitive entropy calibration.

Qiannian Zhao, Chen Yang, Jinhao Jing +5

RL for Language Model ReasoningLarge Reasoning ModelsLanguage Model CalibrationReinforcement Learning with Verifiable RewardsMetacognition in Language Models
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Feb 26, 2026

ContextRL: Enhancing MLLM's Knowledge Discovery Efficiency with Context-Augmented RL

We propose ContextRL, a novel framework that leverages context augmentation to overcome these bottlenecks. Specifically, to enhance Identifiability, we provide the reward model with full reference solutions as context, enabling fine-grained process verification to filter out false positives (samples with the right answer but low-quality reasoning process). To improve Reachability, we introduce a multi-turn sampling strategy where the reward model generates mistake reports for failed attempts, guiding the policy to "recover" correct responses from previously all-negative groups. Experimental results on 11 perception and reasoning benchmarks show that ContextRL significantly improves knowledge discovery efficiency. Notably, ContextRL enables the Qwen3-VL-8B model to achieve performance comparable to the 32B model, outperforming standard RLVR baselines by a large margin while effectively mitigating reward hacking. Our in-depth analysis reveals the significant potential of contextual information for improving reward model accuracy and document the widespread occurrence of reward hacking, offering valuable insights for future RLVR research.

Xingyu Lu, Jinpeng Wang, YiFan Zhang +12

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · Harbin Institute of Technology, Shenzhen, Shenzhen, China · Chinese Academy of Sciences, Beijing, China +2

RL for VLMsReinforcement Learning with Verifiable RewardsIn-Context RLProcess Reward ModelsReward Hacking
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Feb 25, 2026

GUI-Libra: Training Native GUI Agents to Reason and Act with Action-aware Supervision and Partially Verifiable RL

Open-source native GUI agents still lag behind closed-source systems on long-horizon navigation tasks. This gap stems from two limitations: a shortage of high-quality, action-aligned reasoning data, and the direct adoption of generic post-training pipelines that overlook the unique challenges of GUI agents. We identify two fundamental issues in these pipelines: (i) standard SFT with CoT reasoning often hurts grounding, and (ii) step-wise RLVR-tyle training faces partial verifiability, where multiple actions can be correct but only a single demonstrated action is used for verification. This makes offline step-wise metrics weak predictors of online task success. In this work, we present GUI-Libra, a tailored training recipe that addresses these challenges. First, to mitigate the scarcity of action-aligned reasoning data, we introduce a data construction and filtering pipeline and release a curated 81K GUI reasoning dataset. Second, to reconcile reasoning with grounding, we propose action-aware SFT that mixes reasoning-then-action and direct-action data and reweights tokens to emphasize action and grounding. Third, to stabilize RL under partial verifiability, we identify the overlooked importance of KL regularization in RLVR and show that a KL trust region is critical for improving offline-to-online predictability; we further introduce success-adaptive scaling to downweight unreliable negative gradients. Across diverse web and mobile benchmarks, GUI-Libra consistently improves both step-wise accuracy and end-to-end task completion. Our results suggest that carefully designed post-training and data curation can unlock significantly stronger task-solving capabilities without costly online data collection. We release our dataset, code, and models to facilitate further research on data-efficient post-training for reasoning-capable GUI agents.

Rui Yang, Qianhui Wu, Zhaoyang Wang +8

UIUC · Microsoft · UNC-Chapel Hill

GUI AgentsRL for GUI AgentsSupervised Fine-TuningReinforcement Learning with Verifiable RewardsKL-Regularized RL
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