Identifiability and generalizability from multiple experts in Inverse Reinforcement Learning
This work addresses the fundamental ill-posedness of IRL for researchers and practitioners, providing theoretical guarantees for reward recovery and generalization, though it is incremental by building on prior identifiability results.
The paper tackles the problem of reward function identifiability in Inverse Reinforcement Learning (IRL) by showing that observing multiple experts with different discount factors or environments allows identification up to a constant under verifiable rank conditions, and extends this to scenarios with linear reward features or approximate transitions, with numerical validation.
While Reinforcement Learning (RL) aims to train an agent from a reward function in a given environment, Inverse Reinforcement Learning (IRL) seeks to recover the reward function from observing an expert's behavior. It is well known that, in general, various reward functions can lead to the same optimal policy, and hence, IRL is ill-defined. However, (Cao et al., 2021) showed that, if we observe two or more experts with different discount factors or acting in different environments, the reward function can under certain conditions be identified up to a constant. This work starts by showing an equivalent identifiability statement from multiple experts in tabular MDPs based on a rank condition, which is easily verifiable and is shown to be also necessary. We then extend our result to various different scenarios, i.e., we characterize reward identifiability in the case where the reward function can be represented as a linear combination of given features, making it more interpretable, or when we have access to approximate transition matrices. Even when the reward is not identifiable, we provide conditions characterizing when data on multiple experts in a given environment allows to generalize and train an optimal agent in a new environment. Our theoretical results on reward identifiability and generalizability are validated in various numerical experiments.