Geometric-Mean Policy Optimization
Abstract
Group Relative Policy Optimization (GRPO) has significantly enhanced the reasoning capability of large language models by optimizing the arithmetic mean of token-level rewards. Unfortunately, GRPO is observed to suffer from unstable policy updates when facing tokens with outlier importance-weighted rewards, which manifest as extreme importance sampling ratios during training. In this study, we propose Geometric-Mean Policy Optimization (GMPO), with the aim to improve the stability of GRPO through suppressing token reward outliers. GMPO is plug-and-play—simply replacing GRPO's arithmetic mean with the geometric mean of token-level rewards, as the latter is inherently less sensitive to outliers. GMPO is theoretically plausible—analysis reveals that both GMPO and GRPO are weighted forms of the policy gradient while the former enjoys more stable weights, which consequently benefits policy optimization and performance. Experiments on multiple mathematical reasoning benchmarks show that \Ours-7B improves the average Pass@1 of GRPO by up to 4.1%, outperforming many state-of-the-art approaches. Code is available at https://github.com/callsys/GMPO and verl.
Cite
Text
Zhao et al. "Geometric-Mean Policy Optimization." International Conference on Learning Representations, 2026.Markdown
[Zhao et al. "Geometric-Mean Policy Optimization." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/zhao2026iclr-geometricmean/)BibTeX
@inproceedings{zhao2026iclr-geometricmean,
title = {{Geometric-Mean Policy Optimization}},
author = {Zhao, Yuzhong and Liu, Yue and Liu, Junpeng and Chen, Jingye and Wu, Xun and Hao, Yaru and Lv, Tengchao and Huang, Shaohan and Cui, Lei and Ye, Qixiang and Wan, Fang and Wei, Furu},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/zhao2026iclr-geometricmean/}
}