Group Relative Policy Optimization

Also known as GRPO

Group Relative Policy Optimization studies how to improve a model or agent by sampling several responses to the same prompt and using their relative rewards to guide policy updates. Its critic-free, group-normalized approach is widely used for reinforcement learning with verifiable rewards in reasoning tasks such as GSM8K and MATH, and has been adapted to tool-use agents, vision-language models, and diffusion-based image and video generation. Current methods refine reward design and credit assignment, adjust sampling and curricula, and modify normalization, clipping, or entropy controls to improve learning efficiency and stability. A central challenge is that sparse or uniform group rewards can provide little or misleading signal, while choices such as response-length normalization and diversity control can trade off update reliability, exploration, and performance.

Latest papers

343 papers53 papers in the last four weeks, up 33% on the four weeks before. 0.3% of all new papers.

Feb 1, 2026

MedAD-R1: Consistency-Reinforced Policy Optimization for Interpretable Medical Anomaly Detection

Medical Anomaly Detection (MedAD) offers a promising direction for medical image analysis with Large Multimodal Models (LMMs). However, progress is limited by fragmented datasets and the tendency of Supervised Fine-Tuning (SFT) to learn superficial image-text correlations rather than verifiable diagnostic reasoning. Consequently, current models often generate fluent explanations that are either insufficiently grounded in the image or inconsistent with their final answers, limiting their reliability in high-stakes medical applications. To address these issues, we introduce MedAD-38K, a large-scale, multimodal, and multicenter benchmark containing structured Visual Question Answering pairs and quality-controlled diagnostic Chain-of-Thought annotations across five core MedAD tasks. Based on this benchmark, we propose a two-stage framework. Cognitive Injection first uses SFT to inject domain-specific medical knowledge and establish a structured think-then-answer format. Consistency Group Relative Policy Optimization (Con-GRPO) then employs an Evidence-Aware Consistency Reward to reinforce reasoning that remains grounded in the image and logically supports the final answer. The resulting MedAD-R1 achieves state-of-the-art performance on MedAD-38K and consistently outperforms all evaluated baselines across five source-disjoint external datasets spanning diverse imaging modalities. Beyond accuracy, it achieves higher reasoning-answer consistency and visual-grounding scores across multiple backbones. With only 0.8B parameters, MedAD-R1 offers practical potential for resource-constrained deployment. These results demonstrate the generality of evidence-aware consistency optimization for interpretable MedAD. Project resources are available at https://github.com/zhtstar/MedAD-R1.

Haitao Zhang, Yingying Wang, Jiaxiang Wang +5

School of Informatics, Xiamen University · Institute of Artificial Intelligence, Xiamen University · Zhejiang Expressway Co., Ltd. +3

Healthcare Group Relative Policy Optimization Medical Image Anomaly Detection Multimodal Large Language Models Medical Visual Question Answering Multimodal Anomaly Detection+2

Ask PDF

Jan 30, 2026

Why GRPO Needs Normalization: A Local-Curvature Perspective on Adaptive Gradients

Reinforcement learning (RL) has become a key driver of language model reasoning. Among RL algorithms, Group Relative Policy Optimization (GRPO) is the de facto standard, avoiding the need for a critic by using per-prompt baselines and variance normalization. Yet why and when this normalization helps remains unclear. In this work, we answer both questions through the lens of local curvature of the sequence-level policy gradient: standard deviation normalization implements an adaptive gradient. Theoretically, we prove that under mild conditions GRPO attains an improved convergence rate over unnormalized REINFORCE, with gains characterized by the average within-prompt reward standard deviation across prompts and iterations. We further introduce IS-GRPO, an importance-sampling variant of GRPO whose expected update remains aligned with the full gradient, and prove a convergence guarantee of the same form as REINFORCE's, which is tighter in practice during real training runs by a factor we measure. Empirically, on GSM8K and MATH we validate the curvature--variance link and measure the quantities that govern our bounds along real training runs. At 1.5B scale, per-prompt normalization outperforms both unnormalized and globally normalized baselines, with gains that emerge in a middle phase of training where per-prompt variances become heterogeneous. At 7B scale, the normalization schemes become statistically indistinguishable while IS-GRPO retains a small lead, in line with the theory's prediction that the gains require heterogeneity.

Cheng Ge, Caitlyn Heqi Yin, Hao Liang +1

Department of Aeronautics and Astronautics, MIT · Department of Statistics, University of Wisconsin–Madison · Department of Informatics, King’s College London +1

RL for Language Model Reasoning Group Relative Policy Optimization Adaptive Gradient Methods

Ask PDF

Jan 29, 2026

Can David Beat Goliath? On Multi-Hop Reasoning with Resource-Constrained Agents

Reinforcement learning (RL) trains small language model agents to answer multi-hop questions by retrieving evidence over multiple turns, but reported gains typically rely on thousands of on-policy rollouts per update. We study RL for such agents on commodity GPUs, where each update samples only a few rollouts per question. Most sampled trajectories then retrieve none of the required evidence, so the outcome reward gives the policy little to learn from and small agents settle for answering without retrieval, a failure we call retrieval collapse. DAVID-GRPO addresses this with two mechanisms: (1) expert trajectory seeding places a handful of off-policy expert trajectories into the GRPO groups of the early updates, and (2) evidence-guided continuation rewards evidence coverage and resumes the most promising partial trajectory. The evidence for each training question is constructed from the corpus link graph, without annotated evidence. On six multi-hop QA benchmarks, DAVID-GRPO trained on four RTX 3090 GPUs with 144 rollouts per step brings Qwen2.5-1.5B to 22.6 average EM against 11.9 for the best baseline under the same budget, is comparable to Tree-GRPO trained with 20 times more rollouts, and, unlike the baselines that stop after at most one search, learns to retrieve across turns. The implementation is available at: https://github.com/AsadalJung/David-GRPO

Hojae Han, Heeyun Jung, Jongyoon Kim +1

ETRI · The University of Hong Kong · Seoul National University

RL for Language Model Reasoning Multi-Hop QA Sample-Efficient RL RL for IR Group Relative Policy Optimization

Ask PDF

Jan 29, 2026

Expected Return Causes Outcome-Level Mode Collapse in Reinforcement Learning and How to Fix It with Inverse Probability Scaling

Many reinforcement learning (RL) problems admit multiple terminal solutions of comparable quality, where the goal is not to identify a single optimum but to represent a diverse set of high-quality outcomes. Nevertheless, policies trained by standard expected return maximization routinely collapse onto a small subset of outcomes, a phenomenon commonly attributed to insufficient exploration or weak regularization. We show that this explanation is incomplete: outcome level mode collapse is a structural consequence of the expected-return objective itself. Under idealized learning dynamics, the log-probability ratio between any two outcomes evolves linearly in their reward difference, implying exponential ratio divergence and inevitable collapse independent of the exploration strategy, entropy regularization, or optimization algorithm. We identify the source of this pathology as the probability multiplier inside the expectation and propose a minimal correction: inverse probability scaling, which removes outcome-frequency amplification from the learning signal, fundamentally changes the learning dynamics, and provably yields reward-proportional terminal distributions, preventing collapse in multimodal settings. We instantiate this principle in Group Relative Policy Optimization (GRPO) as a drop-in modification, IPS-GRPO, requiring no auxiliary models or architectural changes. Across different reasoning and molecular generation tasks, IPS-GRPO consistently reduces outcome-level mode collapse while matching or exceeding baseline performance, suggesting that correcting the objective rather than adding exploration heuristics is key to reliable multimodal policy optimization.

Abhijeet Sinha, Sundari Elango, Dianbo Liu

National University of Singapore, Singapore · IIT Madras, India

Reinforcement Learning Behavioral Diversity in RL Group Relative Policy Optimization

Ask PDF

Jan 13, 2026

Your Group-Relative Advantage Is Biased

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we characterize conditional estimation bias in group-relative advantages among non-degenerate groups. For mean-centered advantages under binary rewards, our analysis shows negative conditional mean estimation errors for hard prompts and positive errors for easy prompts. At the response level, correct answers to hard prompts are underweighted, while incorrect answers to easy prompts receive insufficient penalties. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Fengkai Yang, Zherui Chen, Xiaohan Wang +10

Beihang University · Peking University · Meituan +1

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Group Relative Policy Optimization

Ask PDF

Jan 11, 2026

GDEPO: Group Dual-dynamic and Equal-right Advantage Policy Optimization for Sample-Efficient Reinforcement Learning

Automated Theorem Proving (ATP) is a fundamental AI challenge, requiring machine-verifiable proofs in formal languages like Lean to evaluate reasoning. Reinforcement Learning (RL), especially Group Relative Policy Optimization (GRPO), is a mainstream approach. However, GRPO faces two critical issues in ATP: its relative advantage estimation may conflict with binary verifier feedback under composite rewards, and its static sampling strategy discards batches without valid proofs, causing data waste. Repeated training on mastered problems also wastes computation. To address this, we propose Group Dual-dynamic and Equal-right Advantage Policy Optimization (GDEPO), incorporating three core mechanisms: 1) dynamic additional sampling, resampling ineffective batches until a valid proof is found; 2) equal-right advantage, decoupling the advantage function's sign (correctness) from its magnitude (auxiliary rewards) to ensure stable policy updates while increasing effective computation; and 3) dynamic additional iterations, applying extra gradient steps to initially failed but eventually successful samples to accelerate learning. Experiments on MinF2F-test, MathOlympiadBench, and PutnamBench confirm GDEPO's effectiveness, with ablation studies validating its synergistic components. The method enhances data utilization and optimization efficiency, offering a novel training paradigm for ATP.

Zhengqing Yan, Fan Guo, Xinyang Liu +5

State Key Laboratory of Engines, Tianjin University, 300354 Tianjin, China. · Artificial Intelligence Center, Cylingo Group, 100080 Beijing, China.

Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards Sample-Efficient RL Automated Theorem Proving

Ask PDF

Nov 24, 2025

Rethinking Reward Signals in Video GRPO: When Scores Become Targets

Group Relative Policy Optimization (GRPO) enables stable and preference-oriented updates via group-wise comparisons for post-training video generation. However, GRPO directly optimizes reward-induced advantages. Under sustained optimization, the reward score can lose fidelity as a proxy for true video quality, consistent with the phenomenon described by Goodhart's Law. This leads to two recurring issues: (i) shortcut-driven optimization under composite objectives and (ii) reward saturation within prompt groups. To address these issues, we introduce TaRoS, a Target-Robust Reward Signaling framework for Video generation GRPO. TaRoS leverages component level performance assessment together with intra-group sparsity to organize multi-aspect rewards towards optimization objectives. In addition, it adaptively downweights components that exhibit saturation, thereby preserving effective optimization directions and mitigating redundancy. This maintains meaningful optimization directions and preserves within-group ranking separation, thereby preventing reward hacking and leading to more reliable policy updates. Extensive experiments show consistent improvements in visual fidelity, motion coherence, and text-video alignment over strong baselines.

Rui Li, Yuanzhi Liang, Ziqi Ni +3

University of Science and Technology of China, Hefei, China · Institute of Artificial Intelligence (TeleAI), China Telecom, Shanghai, China · Southeast University, Nanjing, China

Reward Hacking RL for Video Generation Group Relative Policy Optimization Multimodal Reward Modeling Video Generation

Ask PDF

Oct 9, 2025

SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies converge prematurely, and sample diversity declines, ultimately harming training effectiveness. Existing remedies, including entropy bonuses and clip-based methods, rarely keep entropy within a stable exploration regime and often introduce oscillatory entropy or reward degradation. In this work, we identify a previously overlooked asymmetry in entropy dynamics: under high-temperature sampling, positive and negative samples have opposite effects on policy entropy. Specifically, high-temperature positive samples promote entropy growth, whereas negative samples suppress it. We provide a qualitative theoretical explanation for this phenomenon: when entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive sample updates, indicating that high-temperature positive samples can counteract entropy decay, thereby slowing entropy collapse and potentially reversing it. Motivated by this insight, we propose SCOPE-RL, a stable entropy control framework through a regularization term constructed from temperature-adaptive positive samples. Extensive experiments show that SCOPE-RL consistently outperforms strong RL baselines on both Pass@1 and Pass@k. Our results provide evidence that escaping entropy collapse can improve reasoning performance, while our quantitative empirical analysis further reveals a non-monotonic entropy-performance relationship, with an optimal level of exploration for RL post-training in reasoning LLMs. Our code is available at https://github.com/597358816/SCOPE-RL.

Chen Wang, Zhaochun Li, Jionghao Bai +4

College of Software, Nankai University · Zhongguancun Academy · Beijing Institute of Technology +2

Entropy Collapse in RL Reinforcement Learning RL Post-Training RL for Language Model Reasoning Group Relative Policy Optimization Maximum Entropy RL

Ask PDF

Oct 9, 2025

Group Contrastive Policy Optimization: Learning Beyond the Self-Exploration Limit with Golden Answers

Reinforcement learning with verifiable rewards (RLVR) has become a powerful paradigm for improving the reasoning abilities of large language models, yet group-based methods lose their learning signal when every sampled response receives zero reward. We propose Group Contrastive Policy Optimization (GCPO), a hybrid objective that preserves standard on-policy optimization for informative rollout groups and activates a proximal contrastive objective only when exploration completely fails. The auxiliary objective pairs an offline golden reasoning trajectory with the current policy's failed responses, thereby providing a reliable positive reference and prompt-specific hard negatives without treating the golden trajectory as an on-policy rollout. Its old-policy token probabilities are evaluated through teacher forcing and used solely to constrain the update, rather than as an importance-sampling correction for the teacher distribution. A first-order analysis shows that the resulting update increases a length-normalized likelihood margin between reliable reasoning and observed failures. Experiments across two model scales and 10 core mathematical reasoning benchmarks demonstrate that GCPO improves training efficiency and final reasoning performance over competitive supervised and RLVR baselines.

Hao Wu, Wei Liu, Shizhe Xiang +3

RL for Language Model Reasoning LLM Reasoning Reinforcement Learning with Verifiable Rewards Contrastive RL Group Relative Policy Optimization

Ask PDF

Sep 30, 2025

Improving Sampling Efficiency in RLVR through Adaptive Rollout and Response Reuse

Group relative policy optimization (GRPO) trains large language models with verifiable rewards by normalizing rewards within response groups. When every response in a group receives the same reward, the advantages vanish and the group provides no policy gradient signal. We propose Adaptive Rollout and Response Reuse Policy Optimization (AR3PO) to obtain informative groups with fewer generations. Adaptive rollout samples responses to each prompt in stages and stops sampling once the model generates a correct response. If all sampled responses are incorrect, response reuse replaces one of them with a past correct response to the same prompt, when available, and recomputes the group advantages. Policy-recomputed reuse trains on the updated groups using probabilities recomputed under the rollout policy; advantage-only reuse uses historical responses only to compute advantages. Across four mathematical benchmarks with 7B and 8B models, AR3PO consistently improves over GRPO and achieves performance comparable to DAPO while requiring up to

4.2\times

fewer generated responses. Experiments with a 32B model also show comparable performance to DAPO at a similar training stage with substantially fewer generated responses.

Yuheng Zhang, Wenlin Yao, Changlong Yu +5

University of Illinois Urbana-Champaign · Amazon

RL for Language Models Reinforcement Learning with Verifiable Rewards Sample-Efficient RL Group Relative Policy Optimization

Ask PDF

Aug 4, 2025

TIC-GRPO: Provable and Efficient Optimization for Reinforcement Learning from Human Feedback

Group Relative Policy Optimization (GRPO) trains language models without a value critic using rewards centered within sampled response groups. We study how importance weighting, clipping, and length normalization affect its stochastic updates and propose Trajectory-level Importance-Corrected GRPO (TIC-GRPO), combining an upper importance-ratio cap with a full-trajectory likelihood ratio. Under common maximum-length normalization, a trajectory change of measure gives a score second moment proportional to the response horizon. We propagate this estimate through the actual empirical baseline and all inner updates. With separately optimized constant steps, the sampling term in TIC's stationarity bound has a linear horizon coefficient, versus order three halves for token-level GRPO

_2

. Matching upper and lower bounds separate the capped methods' worst-case response-level variances by a factor

T

. The bounds track prompt count, response-group size, vocabulary size, reward scale, and score regularity; per-response-normalized GRPO also retains a length-covariance term. Experiments at two Qwen3 scales on four reasoning and coding benchmarks evaluate both mechanisms in sampled-token-normalized training.

Lei Pang, Jun Luo, Ruinan Jin

Peking University Beijing, China · The Ohio State University Columbus, USA · Mohamed bin Zayed University of Artificial Intelligence Abu Dhabi, UAE

Importance Sampling for RL RL for Language Models Group Relative Policy Optimization Policy Optimization RL from Human Feedback

Ask PDF

Jul 29, 2025

MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE

Although GRPO substantially enhances flow matching models in human preference alignment of image generation, methods such as FlowGRPO and DanceGRPO still exhibit inefficiency due to the necessity of sampling and optimizing over all denoising steps specified by the Markov Decision Process (MDP). In this paper, we propose

\textbf{MixGRPO}

, a novel framework that leverages the flexibility of mixed sampling strategies through the integration of stochastic differential equations (SDE) and ordinary differential equations (ODE). This streamlines the optimization process within the MDP to improve efficiency and boost performance. Specifically, MixGRPO introduces a sliding window mechanism, using SDE sampling and GRPO-guided optimization only within the window, while applying ODE sampling outside. This design confines sampling randomness to the time-steps within the window, thereby reducing the optimization overhead, and allowing for more focused gradient updates to accelerate convergence. Additionally, as time-steps beyond the sliding window are not involved in optimization, higher-order solvers are supported for faster sampling. So we present a faster variant, termed

\textbf{MixGRPO-Flash}

, which further improves training efficiency while achieving comparable performance. MixGRPO exhibits substantial gains across multiple dimensions of human preference alignment, outperforming DanceGRPO in both effectiveness and efficiency, with nearly 50% lower training time. Notably, MixGRPO-Flash further reduces training time by 71%.

Junzhe Li, Yutao Cui, Tao Huang +8

Hunyuan, Tencent, China · School of Computer Science, Peking University, China · Computer Center, Peking University, China +2

Diffusion Model Alignment Flow Matching Group Relative Policy Optimization Diffusion Sampling RL for Diffusion Models

Ask PDF

Jun 24, 2025

HiMA-Ecom: A Long-Horizon Memory Benchmark for Hierarchical Multi-Agent E-commerce Assistants

Long-horizon agentic systems become long-context systems by accumulation rather than through a single long document, since every step reassembles a prompt from role instructions, tool and sub-agent descriptions, recalled memories, dialogue history, and previous tool outputs, separately for every agent. This paper studies how such accumulated context can be trained, evaluated, and managed in hierarchical multi-agent assistants. We present HiMA-Ecom, a hierarchical multi-agent benchmark for e-commerce assistants with 22.8K instances, of which 17.7K carry memory entries in context, pairing agent-specific supervised fine-tuning data with system-level supervision for end-to-end multi-agent reinforcement learning. Building upon it, HiMA-R1 keeps the context budget of a trajectory under control through Variance-Reduction Group Relative Policy Optimization (VR-GRPO), which samples along an initial trajectory so that sampling cost grows additively with trajectory length and updates the agents with the largest reward variance, together with an efficiency reward on trajectory length and a memory evolution mechanism that repurposes GRPO rewards as cost-free signals for what stays in context. Agents built upon 3B and 7B open-source models match DeepSeek-R1 and surpass DeepSeek-V3 by 6.0 points on average, while reward-driven memory reduces the update steps needed for convergence by roughly 55%.

Junxing Hu, Ai Han, Haolan Zhan +8

JD Retail, JD.com, Inc., Beijing, 101111, China · Faculty of Engineering and Information Technology, The University of Melbourne, Parkville, Victoria, 3082, Australia · School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

Hierarchical MARL Long-Horizon Agent Evaluation AI Agent Benchmarks Memory Management for LLM Agents Multi-Agent Reinforcement Learning Group Relative Policy Optimization

Ask PDF