# Learning Reasoning Rewards from Expert Demonstrations with Inverse Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.01857 · HTML: https://mlsanity.com/paper/2510.01857/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 27 of 27)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [MedReason: Eliciting Factual Medical Reasoning Steps in LLMs via Knowledge Graphs](https://mlsanity.com/paper/2504.00993/) (2025)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)
- [Efficient Knowledge Injection in LLMs via Self-Distillation](https://mlsanity.com/paper/2412.14964/) (2024)

## Built on by (most cited first, 1 of 1)

- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)

## Abstract (arXiv)

Teaching large language models (LLMs) to reason during post-training typically relies on reinforcement learning with explicit outcome- or process-based reward functions. However, in many real-world settings, obtaining or defining such reward functions is difficult, especially for complex tasks, making learning from expert demonstrations an attractive alternative. The dominant approach, supervised fine-tuning (SFT), trains models to imitate expert reasoning traces directly, but suffers from the general limitations of off-policy learning: performance can be fragile to inference-time deviations from states explicitly covered by the demonstrations. To address this, we propose Reasoning Adversarial Inverse Reinforcement Learning (R-AIRL). Rather than imitating the expert's reasoning, R-AIRL infers the underlying process-level reward from the expert Chain-of-Thoughts. Through experiments on GSM8K, MMLU-Pro and MedReason we show that the reasoning reward function learned with R-AIRL can be effectively used throughout the training and inference pipeline: (1) to provide a training signal for post-training, outperforming SFT in most of the considered settings, (2) for inference-time reranking, improving pass@1 by up to 17.4 points, and (3) for process-level evaluation, localising reasoning failures with up to 86.1% accuracy. Overall, R-AIRL bridges imitation learning and reward-based optimisation, enabling the extraction of meaningful reasoning signals from expert thinking traces.