In several problems of interest, it is possible to observe the behavior of multiple agents with different degrees of expertise .

Inverse Reinforcement Learning (IRL) deals with the problem of deducing a reward function that explains the behavior of an expert agent who is assumed to act in an underlying unknown task. Recent works have studied the IRL problem from the perspective of recovering the, i.e., the class of reward functions that are compatible with a unique optimal expert. However, in several problems of interest 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 focus on the reconstruction of the feasible reward set when, in addition to demonstrations from the optimal expert, we observe the behavior of multiple . Given this problem, we first study the theoretical properties showing that the presence of multiple sub-optimal experts, in addition to the optimal one, can significantly shrink the set of compatible rewards, ultimately mitigating the inherent ambiguity of IRL.Furthermore, we study the statistical complexity of estimating the feasible reward set with a generative model and analyze a uniform sampling algorithm that turns out to be minimax optimal whenever the sub-optimal experts' performance level is sufficiently close to that of the optimal expert.

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.