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

arXiv: https://arxiv.org/abs/2003.03709 · HTML: https://mlsanity.com/paper/2003.03709/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 8 Mar 2020.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 19 of 19)

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Provably Efficient Exploration in Policy Optimization](https://mlsanity.com/paper/1912.05830/) (2019)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies](https://mlsanity.com/paper/1906.08383/) (2019)
- [Imitating Driver Behavior with Generative Adversarial Networks](https://mlsanity.com/paper/1701.06699/) (2017)
- [Learning human behaviors from motion capture by adversarial imitation](https://mlsanity.com/paper/1707.02201/) (2017)
- [Sample Efficient Policy Gradient Methods with Recursive Variance Reduction](https://mlsanity.com/paper/1909.08610/) (2019)
- [An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradient](https://mlsanity.com/paper/1905.12615/) (2019)
- [Socially Compliant Navigation through Raw Depth Inputs with Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1710.02543/) (2017)
- [Neural Proximal/Trust Region Policy Optimization Attains Globally Optimal Policy](https://mlsanity.com/paper/1906.10306/) (2019)
- [Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games](https://mlsanity.com/paper/1906.00729/) (2019)
- [On Computation and Generalization of Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2001.02792/) (2020)
- [On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator](https://mlsanity.com/paper/1901.03674/) (2019)

## Built on by (most cited first, 7 of 7)

- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [Online Apprenticeship Learning](https://mlsanity.com/paper/2102.06924/) (2021)
- [When Will Generative Adversarial Imitation Learning Algorithms Attain Global Convergence](https://mlsanity.com/paper/2006.13506/) (2020)
- [Efficient Performance Bounds for Primal-Dual Reinforcement Learning from Demonstrations](https://mlsanity.com/paper/2112.14004/) (2021)
- [Goal-Aware Generative Adversarial Imitation Learning from Imperfect Demonstration for Robotic Cloth Manipulation](https://mlsanity.com/paper/2209.10149/) (2022)
- [Model-Based Imitation Learning Using Entropy Regularization of Model and Policy](https://mlsanity.com/paper/2206.10101/) (2022)
- [Understanding Inverse Reinforcement Learning under Overparameterization: Non-Asymptotic Analysis and Global Optimality](https://mlsanity.com/paper/2503.17865/) (2025)

## Abstract (arXiv)

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.