发表机构
Federal University of Bahia（巴伊亚联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出GA-GRPO统一框架，将外部引导建模为随机算子，给出收敛速率与最优权重闭式解，实验证明其性能优于现有方法且节省31%计算资源。
AI 中文摘要
基于可验证奖励的强化学习（RLVR）已成为在大语言模型中激发多步推理的主导范式，最近一系列方法（LUFFY、ExPO、PAPO、TAPO）进一步用外部引导（专家轨迹、自我解释或检索到的思维模式）增强强化学习。尽管每种方法都报告了经验上的提升，但均未提供收敛速率、偏差界限或引导信号的最优加权规则。我们通过引导增强GRPO（GA-GRPO）填补了这一空白，这是一个统一的理论框架，将外部引导视为一个随机引导算子G，重写问题分布，并将由此产生的策略梯度估计器分析为有偏的在线策略估计器，其偏差由引导增强采样分布与策略自身分布之间的全变差引导散度delta_G界定。该框架将原始GRPO、LUFFY、ExPO、PAPO和TAPO作为通过特定选择G得到的特例。在平滑性和有界散度假定下，我们证明GA-GRPO以O(1/sqrt(T))的速率收敛到GRPO驻点的O(delta sqrt(T))邻域，推导出闭式均方误差最优引导权重lambda-star(T, delta, sigma_0^2) = sigma_0^2 / (sigma_0^2 + R_max^2 delta^2 T)，并证明匹配的极小极大下界，表明Omega(delta^2 T)偏差项不可避免。在Qwen2.5-Math-7B-Base上跨九个数学和OOD基准的实验证实，最优权重的GA-GRPO匹配或超越TAPO、LUFFY、ExPO和原始GRPO，同时所需GPU小时数减少31%，八项分析实验验证了每个理论预测。
英文摘要
Reinforcement learning with verifiable rewards (RLVR) has become the dominant paradigm for eliciting multi-step reasoning in large language models, and a recent wave of methods (LUFFY, ExPO, PAPO, TAPO) further augments RL with \emph{external guidance} - expert traces, self-explanations, or retrieved thought patterns. Although each method reports empirical gains, none provides convergence rates, bias bounds, or an optimal weighting rule for the guidance signal. We close this gap with \emph{Guidance-Augmented GRPO} (GA-GRPO), a unified theoretical framework that casts external guidance as a stochastic guidance operator G re-writing the question distribution, and analyses the resulting policy-gradient estimator as a biased on-policy estimator whose bias is bounded by the total-variation guidance divergence delta\_G between the guidance-augmented sampling distribution and the policy's own distribution. The framework subsumes vanilla GRPO, LUFFY, ExPO, PAPO, and TAPO as special cases obtained by particular choices of G. Under smoothness and bounded-divergence assumptions we prove that GA-GRPO converges at rate O(1/sqrt(T)) to an O(delta sqrt(T))-neighbourhood of the GRPO stationary point, derive the closed-form MSE-optimal guidance weight lambda-star(T, delta, sigma\_0 squared) = sigma\_0 squared / (sigma\_0 squared + R\_max squared delta squared T), and prove a matching minimax lower bound showing the Omega(delta squared T) bias term is unavoidable. Experiments on Qwen2.5-Math-7B-Base across nine math and OOD benchmarks confirm that optimal-weight GA-GRPO matches or surpasses TAPO, LUFFY, ExPO, and vanilla GRPO while requiring 31\% fewer GPU-hours, and eight analysis experiments validate each theoretical prediction.
