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

arXiv: https://arxiv.org/abs/2507.02834 · HTML: https://mlsanity.com/paper/2507.02834/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Meta-Rewarding Language Models: Self-Improving Alignment with LLM-as-a-Meta-Judge](https://mlsanity.com/paper/2407.19594/) (2024)
- [Recursive Introspection: Teaching Language Model Agents How to Self-Improve](https://mlsanity.com/paper/2407.18219/) (2024)
- [A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce](https://mlsanity.com/paper/2504.11343/) (2025)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening](https://mlsanity.com/paper/2506.02355/) (2025)
- [Training Chain-of-Thought via Latent-Variable Inference](https://mlsanity.com/paper/2312.02179/) (2023)

## Built on by (most cited first, 13 of 13)

- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Aligning Language Models from User Interactions](https://mlsanity.com/paper/2603.12273/) (2026)
- [Nudging the Boundaries of LLM Reasoning](https://mlsanity.com/paper/2509.25666/) (2025)
- [Representation-Based Exploration for Language Models: From Test-Time to Post-Training](https://mlsanity.com/paper/2510.11686/) (2025)
- [RAVR: Reference-Answer-guided Variational Reasoning for Large Language Models](https://mlsanity.com/paper/2510.25206/) (2025)
- [Learning Robust Reasoning through Guided Adversarial Self-Play](https://mlsanity.com/paper/2602.00173/) (2026)
- [Beyond Unimodal Shortcuts: MLLMs as Cross-Modal Reasoners for Grounded Named Entity Recognition](https://mlsanity.com/paper/2602.04486/) (2026)
- [Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning](https://mlsanity.com/paper/2604.07941/) (2026)
- [Off-Trajectory Reasoning: Can LLMs Collaborate on Reasoning Trajectory?](https://mlsanity.com/paper/2510.06410/) (2025)
- [Masked Distillation: Internalizing the Chain-of-Thought in Language Models](https://mlsanity.com/paper/2607.22629/) (2026)
- [Chart Deep Research in LVLMs via Parallel Relative Policy Optimization](https://mlsanity.com/paper/2603.06677/) (2026)
- [Evolutionary Task Discovery: Advancing Reasoning Frontiers via Skill Composition and Complexity Scaling](https://mlsanity.com/paper/2605.11666/) (2026)
- [When Does External Guidance Help LLM Reasoning? A Bias-Variance Theory of Guidance-Augmented GRPO](https://mlsanity.com/paper/2610.06861/) (2026)

## Abstract (arXiv)

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 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/ExPOrlreasoningbyexplanation .