Generative Adversarial Imitation Learning with Neural Networks: Global Optimality and Convergence Rate

TL;DR

This paper provides the first theoretical analysis demonstrating that GAIL with neural networks converges to a globally optimal solution at a sublinear rate, bridging the gap between empirical success and theoretical understanding.

Contribution

It establishes the global optimality and convergence rate of GAIL with neural networks, addressing a key theoretical gap in the understanding of this method.

Findings

Proves sublinear convergence of a gradient-based GAIL algorithm.

Establishes global optimality of GAIL with neural networks.

Bridges the gap between empirical success and theoretical guarantees.

Abstract

Generative adversarial imitation learning (GAIL) demonstrates tremendous success in practice, especially when combined with neural networks. Different from reinforcement learning, GAIL learns both policy and reward function from expert (human) demonstration. Despite its empirical success, it remains unclear whether GAIL with neural networks converges to the globally optimal solution. The major difficulty comes from the nonconvex-nonconcave minimax optimization structure. To bridge the gap between practice and theory, we analyze a gradient-based algorithm with alternating updates and establish its sublinear convergence to the globally optimal solution. To the best of our knowledge, our analysis establishes the global optimality and convergence rate of GAIL with neural networks for the first time.