Generalizing Preference-based Reinforcement Learning: a Rationality Model for Incomparability

In this work, we study the reinforcement learning (RL) problem from pairwise trajectory comparisons provided by a human expert. We generalize preference-based RL by formalizing a novel setting in which the expert can also label trajectory pairs as incomparable, i.e., when neither trajectory dominates the other. We introduce the learning problem and the desiderata that its solution should satisfy. Then, we propose a novel Bradley-Terry-inspired rationality model that effectively captures incomparabilities and infers a multi-dimensional reward function, and we study its properties. We provide a sample complexity analysis for learning the model parameters when a dataset is available. Finally, we evaluate our model's ability to reconstruct a reward function that aligns with the expert's comparisons in simulated environments and to recover the Pareto frontier of policies, along with a robustness analysis across varying levels of expert rationality.