A hybrid deep learning method for finite-horizon mean-field game problems
Abstract
This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved; two numerical examples are provided to illustrate the results.
Cite
@article{arxiv.2310.18968,
title = {A hybrid deep learning method for finite-horizon mean-field game problems},
author = {Yu Zhang and Zhuo Jin and Jiaqin Wei and George Yin},
journal= {arXiv preprint arXiv:2310.18968},
year = {2024}
}