Critique-GRPO: Advancing LLM Reasoning with Natural Language and
  Numerical Feedback
Authors: name: Xiaoying Zhang, name: Hao Sun, name: Yipeng Zhang, name: Kaituo Feng, name: Chaochao Lu, name: Chao Yang, name: Helen Meng

Recent advances in reinforcement learning (RL) with numerical feedback, such
as scalar rewards, have significantly enhanced the complex reasoning
capabilities of large language models (LLMs). Despite this success, we identify
three key challenges encountered by RL with solely numerical feedback:
performance plateaus, limited effectiveness of self-reflection, and persistent
failures. We then demonstrate that RL-finetuned models, even after exhibiting
performance plateaus, can generate correct refinements on persistently failed
problems by leveraging natural language feedback in the form of critiques.
Building on this insight, we propose Critique-GRPO, an online RL framework that
integrates both natural language and numerical feedback for effective policy
optimization. Critique-GRPO enables LLMs to learn from initial responses and
critique-guided refinements simultaneously while maintaining exploration.
Extensive experiments using Qwen2.5-7B-Base and Qwen3-8B-Base show that
Critique-GRPO consistently outperforms supervised learning-based and RL-based
fine-tuning approaches across eight challenging mathematical, STEM, and general
reasoning tasks, improving average pass@1 scores by approximately 4.5% and 5%,
respectively. Notably, Critique-GRPO surpasses a strong baseline that
incorporates expert demonstrations within online RL. Further analysis reveals
two critical insights about policy exploration: (1) higher entropy does not
always guarantee efficient learning from exploration, and (2) longer responses
do not necessarily lead to more effective exploration.