A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation
Abstract
Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a neural Q-learning algorithm, where the data are generated from a Markov decision process, and the action-value function is approximated by a deep ReLU neural network. We prove that neural Q-learning finds the optimal policy with an $O(1/\sqrt{T})$ convergence rate if the neural function approximator is sufficiently overparameterized, where $T$ is the number of iterations. To our best knowledge, our result is the first finite-time analysis of neural Q-learning under non-i.i.d. data assumption.
BibTeX
@InProceedings{pmlr-v119-xu20c,
title = {A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation},
author = {Xu, Pan and Gu, Quanquan},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {10555--10565},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/xu20c/xu20c.pdf},
url = {https://proceedings.mlr.press/v119/xu20c.html},
abstract = {Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a neural Q-learning algorithm, where the data are generated from a Markov decision process, and the action-value function is approximated by a deep ReLU neural network. We prove that neural Q-learning finds the optimal policy with an $O(1/\sqrt{T})$ convergence rate if the neural function approximator is sufficiently overparameterized, where $T$ is the number of iterations. To our best knowledge, our result is the first finite-time analysis of neural Q-learning under non-i.i.d. data assumption.}
}