Identifiability and generalizability from multiple experts in Inverse Reinforcement Learning

TL;DR

This paper investigates the conditions under which reward functions in Inverse Reinforcement Learning can be uniquely identified from multiple experts' behaviors and explores how this knowledge can be used to generalize to new environments.

Contribution

It provides a verifiable rank condition for reward identifiability in tabular MDPs and extends the analysis to feature-based rewards and approximate transition models.

Findings

Reward functions can be identified up to a constant with multiple experts under certain conditions.

The rank condition for identifiability is necessary and sufficient.

Data on multiple experts enables policy generalization to new environments.

Abstract

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.