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arXiv 2610.22263cs.LG
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策略梯度估计中的基线与得分中心化

Baselines and Score Centering in Policy Gradient Estimation

University of Illinois Chicago(伊利诺伊大学芝加哥分校);Perplexity AI(Perplexity AI公司)

Shuo Han, Ziqing Hu

AI总结:

本研究针对强化学习中策略梯度估计的基线与得分中心化问题,提出协方差视角,明确两种中心化方式的差异及在不同重要性采样级别下的适用性。

摘要:

强化学习已成为训练后大型语言模型的广泛应用方法。在典型实现中,学习是离线策略的:生成响应的策略与被训练的策略不同,原因在于训练-推理不匹配或异步训练中的策略陈旧性。这种差异通常通过重要性采样解决,其比率在实践中通常通过截断、掩码或裁剪进行正则化。在正则化重要性采样下,重要性加权策略梯度不再对奖励的恒定偏移具有不变性。通过使用奖励与重要性加权得分之间的协方差作为估计量,可恢复该不变性,当比率未被正则化时,该估计量与策略梯度一致。本说明针对序列级和 token 级重要性采样,提出了这一协方差视角。该视角揭示了组均值基线和得分中心化在策略梯度估计中的作用:两者均在协方差估计中执行中心化,但所减去的均值不同——组均值基线使用样本均值,而得分中心化使用总体均值。两者产生具有不同方差的不同无偏协方差估计量。是否应同时使用这两种形式的中心化,取决于重要性采样是应用于序列级还是 token 级:对于序列级重要性采样,使用组均值基线后,得分中心化无额外益处;对于 token 级重要性采样,当重要性比率被正则化时,仅使用组均值基线而不使用得分中心化通常会引入偏差。

英文摘要:

Reinforcement learning has become a widely used approach to post-training large language models. In a typical implementation, learning is off-policy: The policy generating the responses differs from the policy being trained because of training-inference mismatch or policy staleness in asynchronous training. This discrepancy is commonly addressed by importance sampling, whose ratio is usually regularized in practice through truncation, masking, or clipping. Under regularized importance sampling, the importance-weighted policy gradient is no longer invariant to constant shifts in the reward. This invariance is recovered by using the covariance between the reward and the importance-weighted score as the estimand, which coincides with the policy gradient when the ratio is not regularized. This note develops this covariance perspective for both sequence-level and token-level importance sampling. The covariance perspective reveals the roles of the group-mean baseline and score centering in policy gradient estimation. Both perform centering in covariance estimation, but they differ in the mean being subtracted: The group-mean baseline uses a sample mean, whereas score centering uses a population mean. The two lead to distinct unbiased covariance estimators with different variances. Whether both forms of centering should be used simultaneously depends on whether importance sampling is applied at the sequence level or at the token level. With sequence-level importance sampling, score centering adds no benefit once the group-mean baseline is used; with token-level importance sampling, using the group-mean baseline without score centering generally introduces bias when the importance ratio is regularized.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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