# Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback

arXiv: https://arxiv.org/abs/2506.03106 · HTML: https://mlsanity.com/paper/2506.03106/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Inference-Time Scaling for Generalist Reward Modeling](https://mlsanity.com/paper/2504.02495/) (2025)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Learning from Dialogue after Deployment: Feed Yourself, Chatbot!](https://mlsanity.com/paper/1901.05415/) (2019)
- [Self-Alignment for Factuality: Mitigating Hallucinations in LLMs via Self-Evaluation](https://mlsanity.com/paper/2402.09267/) (2024)
- [J1: Incentivizing Thinking in LLM-as-a-Judge via Reinforcement Learning](https://mlsanity.com/paper/2505.10320/) (2025)
- [Critique Fine-Tuning: Learning to Critique is More Effective than Learning to Imitate](https://mlsanity.com/paper/2501.17703/) (2025)
- [Enhancing LLM Reasoning via Critique Models with Test-Time and Training-Time Supervision](https://mlsanity.com/paper/2411.16579/) (2024)
- [SGP-TOD: Building Task Bots Effortlessly via Schema-Guided LLM Prompting](https://mlsanity.com/paper/2305.09067/) (2023)
- [Evaluating and Steering Modality Preferences in Multimodal Large Language Model](https://mlsanity.com/paper/2505.20977/) (2025)
- [Self-Tuning: Instructing LLMs to Effectively Acquire New Knowledge through Self-Teaching](https://mlsanity.com/paper/2406.06326/) (2024)
- [ThinkLess: A Training-Free Inference-Efficient Method for Reducing Reasoning Redundancy](https://mlsanity.com/paper/2505.15684/) (2025)

## Built on by (most cited first, 30 of 90)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [OneThinker: All-in-one Reasoning Model for Image and Video](https://mlsanity.com/paper/2512.03043/) (2025)
- [Expanding the Capabilities of Reinforcement Learning via Text Feedback](https://mlsanity.com/paper/2602.02482/) (2026)
- [Skill1: Unified Evolution of Skill-Augmented Agents via Reinforcement Learning](https://mlsanity.com/paper/2605.06130/) (2026)
- [Gen-Searcher: Reinforcing Agentic Search for Image Generation](https://mlsanity.com/paper/2603.28767/) (2026)
- [CAPO: Towards Enhancing LLM Reasoning through Generative Credit Assignment](https://mlsanity.com/paper/2508.02298/) (2025)
- [Nudging the Boundaries of LLM Reasoning](https://mlsanity.com/paper/2509.25666/) (2025)
- [EditThinker: Unlocking Iterative Reasoning for Any Image Editor](https://mlsanity.com/paper/2512.05965/) (2025)
- [Reward and Guidance through Rubrics: Promoting Exploration to Improve Multi-Domain Reasoning](https://mlsanity.com/paper/2511.12344/) (2025)
- [AdaTooler-V: Adaptive Tool-Use for Images and Videos](https://mlsanity.com/paper/2512.16918/) (2025)
- [Unleashing VLA Potentials in Autonomous Driving via Explicit Learning from Failures](https://mlsanity.com/paper/2603.01063/) (2026)
- [Language Models Can Learn from Verbal Feedback Without Scalar Rewards](https://mlsanity.com/paper/2509.22638/) (2025)
- [XRPO: Pushing the limits of GRPO with Targeted Exploration and Exploitation](https://mlsanity.com/paper/2510.06672/) (2025)
- [RetroAgent: From Solving to Evolving via Retrospective Dual Intrinsic Feedback](https://mlsanity.com/paper/2603.08561/) (2026)
- [Exploring Reasoning Reward Model for Agents](https://mlsanity.com/paper/2601.22154/) (2026)
- [InT: Self-Proposed Interventions Enable Credit Assignment in LLM Reasoning](https://mlsanity.com/paper/2601.14209/) (2026)
- [CLPO: Curriculum Learning meets Policy Optimization for LLM Reasoning](https://mlsanity.com/paper/2509.25004/) (2025)
- [Rethinking Reward Supervision: Rubric-Conditioned Self-Distillation](https://mlsanity.com/paper/2606.19327/) (2026)
- [R3L: Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification](https://mlsanity.com/paper/2601.03715/) (2026)
- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)
- [Multi-Rollout On-Policy Distillation via Peer Successes and Failures](https://mlsanity.com/paper/2605.12652/) (2026)
- [FastGRPO: Accelerating Policy Optimization via Concurrency-aware Speculative Decoding and Online Draft Learning](https://mlsanity.com/paper/2509.21792/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [The Era of Agentic Organization: Learning to Organize with Language Models](https://mlsanity.com/paper/2510.26658/) (2025)
- [From Solving to Verifying: A Unified Objective for Robust Reasoning in LLMs](https://mlsanity.com/paper/2511.15137/) (2025)
- [Video-R4: Reinforcing Text-Rich Video Reasoning with Visual Rumination](https://mlsanity.com/paper/2511.17490/) (2025)
- [EvoIdeator: Evolving Scientific Ideas through Checklist-Grounded Reinforcement Learning](https://mlsanity.com/paper/2603.21728/) (2026)
- [Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning](https://mlsanity.com/paper/2604.07941/) (2026)
- [Thinking-Free Policy Initialization Makes Distilled Reasoning Models More Effective and Efficient Reasoners](https://mlsanity.com/paper/2509.26226/) (2025)
- [Bootstrapping Exploration with Group-Level Natural Language Feedback in Reinforcement Learning](https://mlsanity.com/paper/2603.04597/) (2026)

## Abstract (arXiv)

Recent advances in reinforcement learning (RL) using numerical rewards have significantly enhanced the complex reasoning capabilities of large language models (LLMs). However, we identify three fundamental limitations of purely numerical feedback: performance plateaus, ineffective spontaneous self-reflection, and persistent failures. We show that plateaued RL models can successfully refine failed solutions when given natural language critiques. Motivated by this, we propose Critique-GRPO, an online RL framework that integrates both natural language and numerical feedback for policy optimization. This approach enables LLMs to learn simultaneously from initial responses and critique-guided refinements, effectively internalizing the exploration benefits of both stages. Extensive experiments show that Critique-GRPO outperforms all compared supervised and RL-based fine-tuning methods, achieving average Pass@1 improvements of approximately +15.0-21.6% on various Qwen models and +7.3% on Llama-3.2-3B-Instruct across eight challenging reasoning tasks. Notably, Critique-GRPO facilitates effective self-improvement through self-critiquing, achieving substantial gains over GRPO, e.g., a +16.7% Pass@1 improvement on AIME 2024. The code and models are released at: https://github.com/zhangxy-2019/critique-GRPO