Adversarial Imitation Learning with General Function Approximation: Theoretical Analysis and Practical Algorithms

TL;DR

This paper introduces OPT-AIL, a new framework for adversarial imitation learning with general function approximation, providing the first provably efficient methods with theoretical guarantees and practical algorithms.

Contribution

It develops a novel optimization-based framework for online AIL with general function approximation, including two concrete methods with theoretical and empirical validation.

Findings

Both OPT-AIL variants achieve polynomial sample and interaction complexity.

OPT-AIL outperforms previous deep AIL methods in challenging tasks.

The methods are practically implementable by optimizing two objectives.

Abstract

Adversarial imitation learning (AIL), a prominent approach in imitation learning, has achieved significant practical success powered by neural network approximation. However, existing theoretical analyses of AIL are primarily confined to simplified settings, such as tabular and linear function approximation, and involve complex algorithmic designs that impede practical implementation. This creates a substantial gap between theory and practice. This paper bridges this gap by exploring the theoretical underpinnings of online AIL with general function approximation. We introduce a novel framework called optimization-based AIL (OPT-AIL), which performs online optimization for reward learning coupled with optimism-regularized optimization for policy learning. Within this framework, we develop two concrete methods: model-free OPT-AIL and model-based OPT-AIL. Our theoretical analysis demonstrates that both variants achieve polynomial expert sample complexity and interaction complexity for learning near-expert policies. To the best of our knowledge, they represent the first provably efficient AIL methods under general function approximation. From a practical standpoint, OPT-AIL requires only the approximate optimization of two objectives, thereby facilitating practical implementation. Empirical studies demonstrate that OPT-AIL outperforms previous state-of-the-art deep AIL methods across several challenging tasks.