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.

本文探讨基于生成式对抗性模型的模仿学习算法（Generative Adversarial Imitation Learning，GAIL）的理论性质，证明了对于一般的回报参数化形式，只要正确控制奖励函数的类别，就可以保证泛化效果，并且利用再生核函数对奖励进行参数化可以使用随机一阶优化算法高效解决，并具有次线性收敛性，这是关于奖励/策略函数逼近的统计和计算保证的第一篇研究。

生成对抗模仿学习的计算与泛化