ExPO: Unlocking Hard Reasoning with Self-Explanation-Guided Reinforcement Learning

Self-improvement via RL often fails on complex reasoning tasks because GRPO-style post-training methods rely on the model's initial ability to generate positive samples. Without guided exploration, these approaches merely reinforce what the model already knows (distribution-sharpening) rather than enabling the model to solve problems where it initially generates no correct solutions. To unlock reasoning ability in such settings, the model must explore new reasoning trajectories beyond its current output distribution. Such exploration requires access to sufficiently good positive samples to guide the learning. While expert demonstrations seem like a natural solution, we find that they are often ineffective in RL post-training. Instead, we identify two key properties of effective positive samples: they should (1) be likely under the current policy, and (2) increase the model's likelihood of predicting the correct answer. Based on these insights, we propose $\textbf{Self-Explanation Policy Optimization (ExPO)}$-a simple and modular framework that generates such samples by conditioning on the ground-truth answer. It can be integrated with popular RL training methods like GRPO and DPO. ExPO enables efficient exploration and guides the model to produce reasoning trajectories more aligned with its policy than expert-written CoTs, while ensuring higher quality than its own (incorrect) samples. Experiments show that ExPO improves both learning efficiency and final performance on reasoning benchmarks, surpassing expert-demonstration-based methods in challenging settings such as MATH level-5, where the model initially struggles the most. Code is available at https://github.com/HumainLab/ExPO_rl_reasoning_by_explanation .