Inverse Reinforcement Learning with Sub-optimal Experts

TL;DR

This paper extends inverse reinforcement learning to incorporate multiple sub-optimal experts, analyzing the feasible reward set and its statistical complexity, with theoretical insights on reward compatibility and optimal sampling strategies.

Contribution

It introduces a novel IRL framework that accounts for sub-optimal experts and characterizes the feasible reward set's properties and estimation complexity.

Findings

Multiple sub-optimal experts reduce the feasible reward set.

The uniform sampling algorithm is minimax optimal under certain conditions.

Theoretical analysis of reward compatibility and statistical complexity.

Abstract

Inverse Reinforcement Learning (IRL) techniques deal with the problem of deducing a reward function that explains the behavior of an expert agent who is assumed to act optimally in an underlying unknown task. In several problems of interest, however, it is possible to observe the behavior of multiple experts with different degree of optimality (e.g., racing drivers whose skills ranges from amateurs to professionals). For this reason, in this work, we extend the IRL formulation to problems where, in addition to demonstrations from the optimal agent, we can observe the behavior of multiple sub-optimal experts. Given this problem, we first study the theoretical properties of the class of reward functions that are compatible with a given set of experts, i.e., the feasible reward set. Our results show that the presence of multiple sub-optimal experts can significantly shrink the set of compatible rewards. Furthermore, we study the statistical complexity of estimating the feasible reward set with a generative model. To this end, we analyze a uniform sampling algorithm that results in being minimax optimal whenever the sub-optimal experts' performance level is sufficiently close to the one of the optimal agent.