提出新奖励估计方法,让语言模型推理训练更省样本、更稳定。
Discounted Beta-Bernoulli Reward Estimation for Sample-Efficient Reinforcement Learning with Verifiable Rewards
- 用历史奖励统计建模非平稳分布,改进奖励估计方式。
- 在6个内分布和3个外分布任务上,准确率平均提升3.22至12.49点。
- 无需额外算力或内存,适合大模型高效微调场景。
基于可验证奖励的强化学习(RLVR)已成为提升大语言模型推理能力的有效后训练范式。然而现有基于分组的RLVR方法常面临严重样本效率低下的问题,根源在于仅依赖少量回滚结果进行奖励点估计,导致估计方差高、方差坍塌及生成响应利用不足。本文从统计估计视角重构RLVR,将奖励视为策略诱导分布的采样结果,把优势计算转化为有限数据下奖励分布的估计问题。在此基础上,提出折扣贝塔-伯努利(DBB)奖励估计方法,利用历史奖励统计处理非平稳分布。尽管存在偏差,该估计器方差更低且更稳定,理论上避免了估计方差坍塌,均方误差低于标准点估计。在六个分布内与三个分布外推理基准上的大量实验表明,采用DBB的GRPO方法始终优于朴素GRPO:在1.7B与8B模型上,分布内平均准确率提升3.22/2.42点,分布外提升12.49/6.92点,且不增加计算成本或内存开销。
原文摘要 · Abstract (English)
Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective post-training paradigm for improving the reasoning capabilities of large language models. However, existing group-based RLVR methods often suffer from severe sample inefficiency. This inefficiency stems from reliance on point estimation of rewards from a small number of rollouts, leading to high estimation variance, variance collapse, and ineffective utilization of generated responses. In this work, we reformulate RLVR from a statistical estimation perspective by modeling rewards as samples drawn from a policy-induced distribution and casting advantage computation as the problem of estimating the reward distribution from finite data. Building on this view, we propose Discounted Beta-Bernoulli (DBB) reward estimation, which leverages historical reward statistics for the non-stationary distribution. Although biased, the resulting estimator exhibits reduced and stable variance, theoretically avoids estimated variance collapse, and achieves lower mean squared error than standard point estimation. Extensive experiments across six in-distribution and three out-of-distribution reasoning benchmarks demonstrate that GRPO with DBB consistently outperforms naive GRPO, achieving average Acc@8 improvements of 3.22/2.42 points in-distribution and 12.49/6.92 points out-of-distribution on the 1.7B and 8B models, respectively, without additional computational cost or memory usage.
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