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arXiv · 2310.18968

A hybrid deep learning method for finite-horizon mean-field game problems

Yu Zhang·Zhuo Jin·Jiaqin Wei·George Yin
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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.

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Yu Zhang, Zhuo Jin, Jiaqin Wei, George Yin. 2023-10-29. A hybrid deep learning method for finite-horizon mean-field game problems. https://arxiv.org/abs/2310.18968

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