Inverse Reinforcement Learning with Sub-optimal Experts
This work addresses a limitation in IRL for real-world scenarios where expert data is imperfect, making it incremental by extending existing formulations to handle sub-optimal demonstrations.
The paper tackles the problem of inverse reinforcement learning when demonstrations come from multiple experts with varying optimality, showing that sub-optimal experts can significantly shrink the set of compatible reward functions and that a uniform sampling algorithm is minimax optimal under certain conditions.
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.