Identifiability and Generalizability in Constrained Inverse Reinforcement Learning

TL;DR

This paper develops a theoretical framework for constrained inverse reinforcement learning, analyzing reward identifiability and generalizability, with implications for safety and transferability in RL.

Contribution

It extends reward identifiability and generalizability results to constrained MDPs and regularizations, highlighting conditions for reward uniqueness and transferability.

Findings

Identifiability up to potential shaping is due to entropy regularization.

Reward must be identified up to a constant for generalization.

Finite sample guarantees for reward suboptimality are provided.

Abstract

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning (IRL) in constrained Markov decision processes. From a convex-analytic perspective, we extend prior results on reward identifiability and generalizability to both the constrained setting and a more general class of regularizations. In particular, we show that identifiability up to potential shaping (Cao et al., 2021) is a consequence of entropy regularization and may generally no longer hold for other regularizations or in the presence of safety constraints. We also show that to ensure generalizability to new transition laws and constraints, the true reward must be identified up to a constant. Additionally, we derive a finite sample guarantee for the suboptimality of the learned rewards, and validate our results in a gridworld environment.