LS-IQ: Implicit Reward Regularization for Inverse Reinforcement Learning

TL;DR

This paper introduces LS-IQ, a novel inverse reinforcement learning method that uses implicit reward regularization, providing theoretical insights and improved stability, especially in environments with absorbing states, and extends to observation-only learning.

Contribution

The paper offers a theoretical analysis of implicit reward regularization in inverse reinforcement learning and proposes LS-IQ, which outperforms existing methods and handles observation-only scenarios.

Findings

LS-IQ outperforms state-of-the-art algorithms in environments with absorbing states.

Theoretical analysis links regularization to squared Bellman error minimization.

Method remains effective with observation-only data, no expert actions needed.

Abstract

Recent methods for imitation learning directly learn a $Q$-function using an implicit reward formulation rather than an explicit reward function. However, these methods generally require implicit reward regularization to improve stability and often mistreat absorbing states. Previous works show that a squared norm regularization on the implicit reward function is effective, but do not provide a theoretical analysis of the resulting properties of the algorithms. In this work, we show that using this regularizer under a mixture distribution of the policy and the expert provides a particularly illuminating perspective: the original objective can be understood as squared Bellman error minimization, and the corresponding optimization problem minimizes a bounded $\chi^2$-Divergence between the expert and the mixture distribution. This perspective allows us to address instabilities and properly treat absorbing states. We show that our method, Least Squares Inverse Q-Learning (LS-IQ), outperforms state-of-the-art algorithms, particularly in environments with absorbing states. Finally, we propose to use an inverse dynamics model to learn from observations only. Using this approach, we retain performance in settings where no expert actions are available.