Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic
Group relative policy optimization (GRPO), a core methodological component of DeepSeekMath and DeepSeek-R1, has emerged as a cornerstone for scaling reasoning capabilities of large language models. Despite its widespread adoption and the proliferation of follow-up works, the theoretical properties of GRPO remain less studied. This paper provides a unified framework to understand GRPO through the lens of classical U-statistics. We demonstrate that the GRPO policy gradient is inherently a U-statistic, allowing us to characterize its mean squared error (MSE), derive the finite-sample error bound and asymptotic distribution of the suboptimality gap for its learned policy. Our findings reveal ...
| Authors | Hongyi Zhou, Kai Ye, Erhan Xu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 March 2026 |
| Last updated at source | 22 March 2026 |
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