Inverse Reinforcement Learning without an Optimal Demonstrator: A Feasible Reward Set Approach

Inverse reinforcement learning (IRL) typically assumes demonstrations from a single optimal demonstrator, but in many applications data come from multiple imperfect demonstrators with heterogeneous suboptimality levels. We study reward learning in this setting through a feasible-reward-set framework: for each demonstrator, we encode its declared suboptimality level as a linear constraint and intersect the resulting feasible sets across demonstrators. Our theoretical analysis shows that the joint feasible set shrinks monotonically as data are added and provides a sufficient condition for strict shrinkage. We further establish optimality guarantees for the unobserved optimal demonstrator under every reward in the resulting feasible set. On the practical side, we introduce strategies to address the inherent reward ambiguity in the obtained reward set and provide an offline algorithm with function approximation for high-dimensional environments. Experiments in tabular grid-world and large language model (LLM) fine-tuning settings support the theoretical predictions and demonstrate improved performance over baselines.