提升大模型数学推理能力,通过动态调节探索强度和智能选题。
expo: Exploration-prioritized policy optimization via adaptive kl regulation and gaussian curriculum sampling
- 根据准确率自适应调整惩罚强度,鼓励模型在困难阶段大胆探索。
- 用高斯分布筛选中等难度题目,让训练聚焦在最有学习价值的问题上。
- 在多个基准测试中显著提升推理性能,尤其在高复杂度任务上优势明显。
强化学习结合可验证奖励(RLVR)已成为大语言模型数学推理的标准范式,其中组相对策略优化(GRPO)是主流算法。本文指出GRPO存在两个未被充分关注的效率问题:一是固定KL惩罚系数过度限制了模型在需要大幅偏离参考策略阶段的探索;二是训练题目均匀采样忽略了中等难度问题能提供最优梯度信号。为此提出探索优先型策略优化(EXPO),包含两个轻量级插件模块:准确率条件KL缩放(AKL)通过批平均准确率的非线性函数动态调节KL正则强度,在模型表现差时放松惩罚、表现好时加强约束;高斯课程采样(GCS)以0.5为中心的高斯分布为题目分配采样权重,聚焦于模型的学习前沿。在DeepSeek-R1-Distill-Qwen-1.5B和Qwen3-8B-Base上对六个数学推理基准进行大量实验,结果表明EXPO持续优于原始GRPO。在AIME 2025 pass@32上绝对提升13.34,从63.33%增至76.67%,8B模型平均pass@32提升2.66。相较于pass@1,pass@32提升更显著,说明EXPO在固定推理成本下有效拓展了模型的探索边界。
原文摘要 · Abstract (English)
Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, where Group Relative Policy Optimization (GRPO) serves as the mainstream algorithm. We point out two understudied inefficiencies existing in GRPO. First, the fixed KL penalty coefficient overly restricts policy exploration at stages where the model requires significant deviation from the reference policy. Second, uniform sampling of training questions ignores that moderately difficult problems provide the most informative gradient signals for optimization. We propose Exploration-Prioritized Policy Optimization (EXPO) with two lightweight plug-in modules. The Accuracy-Conditioned KL Scaling (AKL) dynamically adjusts KL regularization strength through a smooth nonlinear function of batch average accuracy, relaxing the penalty when the model underperforms and strengthening it when the model achieves good results. The Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at moderate accuracy around 0.5, focusing training on the model's learning frontier. We conduct extensive experiments on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base over six mathematical reasoning benchmarks. The results show EXPO steadily surpasses vanilla GRPO. It obtains an absolute gain of 13.34 on AIME 2025 pass@32, rising from 63.33 percent to 76.67 percent, and achieves an average pass@32 improvement of 2.66 on the 8B model. The much larger performance gains on pass@32 compared with pass@1 demonstrate that EXPO effectively enlarges the model's exploration boundary under a fixed inference cost budget.
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