Learning Reasoning Reward Models from Expert Demonstration via Inverse Reinforcement Learning

Current approaches to improving reasoning in large language models (LLMs) primarily rely on either supervised fine-tuning (SFT) over expert traces or reinforcement learning (RL) with outcome-level rewards. However, SFT is fundamentally imitative, while outcome-based RL assumes access to a well-specified verifier. To address this gap, we propose an adversarial inverse reinforcement learning (AIRL) framework that learns reasoning rewards directly from expert demonstrations. We evaluate this framework across reward granularities (sparse, interval, and dense). Granularity controls the resolution of credit assignment: sparse rewards emphasise global trajectory quality and training stability, while denser rewards provide higher-resolution step-level supervision for error localisation but are harder to optimise stably. We show that the learned reasoning rewards are useful in three complementary ways. First, as a training signal, they often outperform SFT, with the best variant improving over SFT on medical reasoning (MedReason), mathematics (GSM8K), and challenging scientific question-answering (MMLU-Pro). Second, as an inference-time reranker, they gain up to 17.4 percentage points under a fixed sampling budget. Third, the learned reward transfers across tasks and backbones, suggesting that part of the signal is reusable beyond a single domain or model, and that finer-grained rewards identify the first step at which a trajectory deviates from a correct path. This supports the diagnosis of reasoning failures and the improvement of test-time selection. Together, these results show that AIRL can recover a reusable intermediate reasoning step from demonstrations alone, bridging the gap between pure imitation and reward-driven optimisation for LLM reasoning.