# On Computation and Generalization of Generative Adversarial Imitation Learning

arXiv: https://arxiv.org/abs/2001.02792 · HTML: https://mlsanity.com/paper/2001.02792/

## Key facts

- Cited by 28 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 18 of its 65 references that are in the map.
- First posted on arXiv 9 Jan 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, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Imitating Driver Behavior with Generative Adversarial Networks](https://mlsanity.com/paper/1701.06699/) (2017)
- [Socially Compliant Navigation through Raw Depth Inputs with Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1710.02543/) (2017)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Reinforced Imitation: Sample Efficient Deep Reinforcement Learning for Map-less Navigation by Leveraging Prior Demonstrations](https://mlsanity.com/paper/1805.07095/) (2018)
- [On gradient regularizers for MMD GANs](https://mlsanity.com/paper/1805.11565/) (2018)
- [On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator](https://mlsanity.com/paper/1901.03674/) (2019)
- [Optimal Primal-Dual Methods for a Class of Saddle Point Problems](https://mlsanity.com/paper/1309.5548/) (2013)
- [SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation](https://mlsanity.com/paper/1712.10285/) (2017)

## Built on by (most cited first, 28 of 28)

- [A Survey on Model-based Reinforcement Learning](https://mlsanity.com/paper/2206.09328/) (2022)
- [Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees](https://mlsanity.com/paper/2210.01808/) (2022)
- [Diffusion Model-Augmented Behavioral Cloning](https://mlsanity.com/paper/2302.13335/) (2023)
- [Rank2Reward: Learning Shaped Reward Functions from Passive Video](https://mlsanity.com/paper/2404.14735/) (2024)
- [Online Apprenticeship Learning](https://mlsanity.com/paper/2102.06924/) (2021)
- [Proximal Point Imitation Learning](https://mlsanity.com/paper/2209.10968/) (2022)
- [When Demonstrations Meet Generative World Models: A Maximum Likelihood Framework for Offline Inverse Reinforcement Learning](https://mlsanity.com/paper/2302.07457/) (2023)
- [Provably Efficient Adversarial Imitation Learning with Unknown Transitions](https://mlsanity.com/paper/2306.06563/) (2023)
- [When Will Generative Adversarial Imitation Learning Algorithms Attain Global Convergence](https://mlsanity.com/paper/2006.13506/) (2020)
- [Understanding Adversarial Imitation Learning in Small Sample Regime: A Stage-coupled Analysis](https://mlsanity.com/paper/2208.01899/) (2022)
- [Structural Estimation of Markov Decision Processes in High-Dimensional State Space with Finite-Time Guarantees](https://mlsanity.com/paper/2210.01282/) (2022)
- [Provably Efficient Generative Adversarial Imitation Learning for Online and Offline Setting with Linear Function Approximation](https://mlsanity.com/paper/2108.08765/) (2021)
- [Efficient Performance Bounds for Primal-Dual Reinforcement Learning from Demonstrations](https://mlsanity.com/paper/2112.14004/) (2021)
- [Making Reconstruction-based Method Great Again for Video Anomaly Detection](https://mlsanity.com/paper/2301.12048/) (2023)
- [Testing for the Markov Property in Time Series via Deep Conditional Generative Learning](https://mlsanity.com/paper/2305.19244/) (2023)
- [Generative Adversarial Imitation Learning with Neural Networks: Global Optimality and Convergence Rate](https://mlsanity.com/paper/2003.03709/) (2020)
- [Wasserstein Flow Meets Replicator Dynamics: A Mean-Field Analysis of Representation Learning in Actor-Critic](https://mlsanity.com/paper/2112.13530/) (2021)
- [OLLIE: Imitation Learning from Offline Pretraining to Online Finetuning](https://mlsanity.com/paper/2405.17477/) (2024)
- [Provably and Practically Efficient Adversarial Imitation Learning with General Function Approximation](https://mlsanity.com/paper/2411.00610/) (2024)
- [Exploring Gradient Explosion in Generative Adversarial Imitation Learning: A Probabilistic Perspective](https://mlsanity.com/paper/2312.11214/) (2023)
- [Revisiting GANs by Best-Response Constraint: Perspective, Methodology, and Application](https://mlsanity.com/paper/2205.10146/) (2022)
- [C-GAIL: Stabilizing Generative Adversarial Imitation Learning with Control Theory](https://mlsanity.com/paper/2402.16349/) (2024)
- [Provably Efficient Off-Policy Adversarial Imitation Learning with Convergence Guarantees](https://mlsanity.com/paper/2405.16668/) (2024)
- [Near-Optimal Second-Order Guarantees for Model-Based Adversarial Imitation Learning](https://mlsanity.com/paper/2510.09487/) (2025)
- [Beyond-Expert Performance with Limited Demonstrations: Efficient Imitation Learning with Double Exploration](https://mlsanity.com/paper/2506.20307/) (2025)
- [Sample-efficient Adversarial Imitation Learning](https://mlsanity.com/paper/2303.07846/) (2023)
- [On Generalization and Distributional Update for Mimicking Observations with Adequate Exploration](https://mlsanity.com/paper/2501.12785/) (2025)
- [Non-Adversarial Imitation Learning Provably Free of Compounding Errors: The Value Flow Mechanism](https://mlsanity.com/paper/2603.22713/) (2026)

## Abstract (arXiv)

Generative Adversarial Imitation Learning (GAIL) is a powerful and practical approach for learning sequential decision-making policies. Different from Reinforcement Learning (RL), GAIL takes advantage of demonstration data by experts (e.g., human), and learns both the policy and reward function of the unknown environment. Despite the significant empirical progresses, the theory behind GAIL is still largely unknown. The major difficulty comes from the underlying temporal dependency of the demonstration data and the minimax computational formulation of GAIL without convex-concave structure. To bridge such a gap between theory and practice, this paper investigates the theoretical properties of GAIL. Specifically, we show: (1) For GAIL with general reward parameterization, the generalization can be guaranteed as long as the class of the reward functions is properly controlled; (2) For GAIL, where the reward is parameterized as a reproducing kernel function, GAIL can be efficiently solved by stochastic first order optimization algorithms, which attain sublinear convergence to a stationary solution. To the best of our knowledge, these are the first results on statistical and computational guarantees of imitation learning with reward/policy function approximation. Numerical experiments are provided to support our analysis.