从推理链到可验证子问题：课程强化学习为LLM推理实现信用分配

摘要

基于可验证奖励的强化学习(RLVR)在大语言模型推理中展现出强大潜力，但基于结果的RLVR在困难问题上效率依然低下，因为正确最终答案的采样稀少，且样本级信用分配无法利用失败尝试中的部分进展。我们提出SCRL（子问题课程强化学习），这是一种课程强化学习框架，能从参考推理链中提取可验证子问题，并将最终子问题设定为原问题。这能将困难问题上的部分进展转化为可验证的学习信号。算法上，SCRL采用子问题层级归一化，即独立地对每个子问题位置进行奖励归一化，并将由此产生的优势值分配给对应的答案片段，从而在不依赖外部评分标准或奖励模型的情况下实现更细粒度的信用分配。我们的分析表明，子问题课程能帮助困难问题摆脱梯度死亡区域，且原问题越难，相对收益越大。在七个数学推理基准上，SCRL的表现优于强课程学习基线：在Qwen3-4B-Base上，平均准确率相比GRPO提升+4.1个百分点；在Qwen3-14B-Base上提升+1.9个百分点。在AIME24、AIME25和IMO-Bench上，SCRL进一步将Qwen3-4B-Base的pass@1提升+3.7个百分点，pass@64提升+4.6个百分点，表明其在困难推理问题上具有更好的探索能力。

English

Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but outcome-based RLVR remains inefficient on hard problems because correct final-answer rollouts are rare and sample-level credit assignment cannot use partial progress in failed attempts. We introduce SCRL (Subproblem Curriculum Reinforcement Learning), a curriculum RL framework that derives verifiable subproblems from reference reasoning chains and fixes the final subproblem as the original problem. This turns partial progress on hard problems into verifiable learning signals. Algorithmically, SCRL uses subproblem-level normalization, which normalizes rewards independently at each subproblem position and assigns the resulting advantages to the corresponding answer spans, enabling finer-grained credit assignment without external rubrics or reward models. Our analysis shows that subproblem curricula lift hard problems out of gradient dead zones, with larger relative gains as the original problem becomes harder. Across seven mathematical reasoning benchmarks, SCRL outperforms strong curriculum-learning baselines, improving average accuracy over GRPO by +4.1 points on Qwen3-4B-Base and +1.9 points on Qwen3-14B-Base. On AIME24, AIME25, and IMO-Bench, SCRL further improves pass@1 by +3.7 points and pass@64 by +4.6 points on Qwen3-4B-Base, indicating better exploration on hard reasoning problems.