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About this paper
Hongcheng Wang, Yinuo Huang, Sukai Wang, Guanghui Ren, Hao Dong
Researchers from Peking University and Agibot theoretically explain why tree-style branching in Group Relative Policy Optimization (GRPO) reduces variance, demonstrating that increasing continuations per thought reduces advantage estimation variance at a rate of 1/M. Their GRPO-MA framework, which samples multiple answers for each semantic thought, consistently improves performance, enhances optimization stability, and offers a better efficiency-performance trade-off across diverse reasoning and multimodal tasks.
Key insights
- A fundamental sampling asymmetry exists: increasing the number of continuations per thought (M) drives the leading-order conditional advantage estimation variance to zero at a rate of 1/M.
- Conversely, simply increasing the number of independently sampled thoughts (K) while keeping M fixed causes the variance to converge to a strictly positive floor, indicating it cannot fully eliminate continuation-level noise.
- For GRPO-style estimators without explicit value models, continuation-level branching is identified as a principled and potentially necessary mechanism for robust variance reduction, rather than just an empirical heuristic.
Summary by alphaXiv.
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