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This paper identifies a critical flaw in the PPO-Clip algorithm used in reinforcement learning for large language models (LLMs), revealing that its reliance on Euclidean metrics leads to exploration collapse. To address this issue, the authors introduce Riemannian Isometric Policy Optimization (RIPO), which aligns policy updates with the intrinsic geometry of the policy Riemannian manifold, thus enhancing exploration and exploitation balance. Experimental results show that RIPO outperforms existing RL algorithms for LLMs, achieving up to a 60% improvement over GRPO on competition-level benchmarks.
RIPO redefines policy optimization for LLMs by correcting a fundamental geometric flaw, leading to unprecedented performance improvements in exploration efficiency.
Reinforcement learning (RL) has become a dominant paradigm for enhancing LLMs'reasoning capabilities. However, RL algorithms with PPO-Clip are inherently limited by exploration collapse. Subsequent works remain primarily heuristic and fail to identify the essential cause of PPO-Clip's failure. This work reveals the fundamental flaw of PPO-Clip: it implicitly measures policy discrepancy using Euclidean metric, which is theoretically inconsistent with the intrinsic geometry on the policy Riemannian manifold. This geometric mismatch results in overly conservative updates in low-probability regions while aggressive in high-probability regions, ultimately collapsing exploration. To correct this geometric flaw, we propose Riemannian Isometric Policy Optimization (RIPO), which guarantees isometric policy updates on the Riemannian manifold, effectively balancing exploration and exploitation. We further show that RIPO achieves a favorable bias-variance trade-off, which stabilizes optimization. Extensive experiments demonstrate that RIPO significantly surpasses existing LLM RL algorithms across seven competition-level benchmarks (up to 60% improvement over GRPO on AIME24).
Tsinghua AI