Robust Imitation via Mirror Descent Inverse Reinforcement Learning

TL;DR

This paper introduces a robust inverse reinforcement learning method based on mirror descent, which improves reward estimation stability and outperforms existing adversarial IRL techniques across benchmarks.

Contribution

It proposes a novel IRL approach using mirror descent that enhances robustness to reward uncertainty and provides theoretical guarantees with regret bounds.

Findings

Outperforms existing adversarial IRL methods in benchmarks

Ensures robust reward minimization with regret bound of O(1/T)

Provides theoretical proof of stability and convergence

Abstract

Recently, adversarial imitation learning has shown a scalable reward acquisition method for inverse reinforcement learning (IRL) problems. However, estimated reward signals often become uncertain and fail to train a reliable statistical model since the existing methods tend to solve hard optimization problems directly. Inspired by a first-order optimization method called mirror descent, this paper proposes to predict a sequence of reward functions, which are iterative solutions for a constrained convex problem. IRL solutions derived by mirror descent are tolerant to the uncertainty incurred by target density estimation since the amount of reward learning is regulated with respect to local geometric constraints. We prove that the proposed mirror descent update rule ensures robust minimization of a Bregman divergence in terms of a rigorous regret bound of $\mathcal{O}(1/T)$ for step sizes $\{\eta_t\}_{t=1}^{T}$. Our IRL method was applied on top of an adversarial framework, and it outperformed existing adversarial methods in an extensive suite of benchmarks.