Paper Detail

Beyond Euclidean Clipping: Overcoming Exploration Collapse in LLM RL via Riemannian Isometric Policy Optimization

Zhicheng Cai, Xinyuan Guo, Hanlin Wu, Mingxuan Wang, Wei-Ying Ma, Ya-Qin Zhang, Hao Zhou

huggingface Score 12.4

Published 2026-07-11 · First seen 2026-07-23

General AI

Abstract

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).

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BibTeX

@misc{cai2026beyond,
  title = {Beyond Euclidean Clipping: Overcoming Exploration Collapse in LLM RL via Riemannian Isometric Policy Optimization},
  author = {Zhicheng Cai and Xinyuan Guo and Hanlin Wu and Mingxuan Wang and Wei-Ying Ma and Ya-Qin Zhang and Hao Zhou},
  year = {2026},
  abstract = {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 Riemanni},
  url = {https://huggingface.co/papers/2607.10169},
  keywords = {code available, huggingface daily},
  eprint = {2607.10169},
  archiveprefix = {arXiv},
}

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