Two system transformation data-driven algorithms for linear quadratic mean-field games

Fuente: arXiv
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Auteurs principaux: Li, Xun, Wang, Guangchen, Wang, Yu, Xiong, Jie, Zhang, Heng
Format: Preprint
Publié: 2024
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author Li, Xun
Wang, Guangchen
Wang, Yu
Xiong, Jie
Zhang, Heng
author_facet Li, Xun
Wang, Guangchen
Wang, Yu
Xiong, Jie
Zhang, Heng
contents This paper studies a class of continuous-time linear quadratic (LQ) mean-field game problems. We develop two system transformation data-driven algorithms to approximate the decentralized strategies of the LQ mean-field games. The main feature of the obtained data-driven algorithms is that they eliminate the requirement on all system matrices. First, we transform the original stochastic system into an ordinary differential equation (ODE). Subsequently, we construct some Kronecker product-based matrices by the input/state data of the ODE. By virtue of these matrices, we implement a model-based policy iteration (PI) algorithm and a model-based value iteration (VI) algorithm in a data-driven fashion. In addition, we also demonstrate the convergence of these two data-driven algorithms under some mild conditions. Finally, we illustrate the practicality of our algorithms via two numerical examples.
format Preprint
id arxiv_https___arxiv_org_abs_2404_10285
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Two system transformation data-driven algorithms for linear quadratic mean-field games
Li, Xun
Wang, Guangchen
Wang, Yu
Xiong, Jie
Zhang, Heng
Optimization and Control
This paper studies a class of continuous-time linear quadratic (LQ) mean-field game problems. We develop two system transformation data-driven algorithms to approximate the decentralized strategies of the LQ mean-field games. The main feature of the obtained data-driven algorithms is that they eliminate the requirement on all system matrices. First, we transform the original stochastic system into an ordinary differential equation (ODE). Subsequently, we construct some Kronecker product-based matrices by the input/state data of the ODE. By virtue of these matrices, we implement a model-based policy iteration (PI) algorithm and a model-based value iteration (VI) algorithm in a data-driven fashion. In addition, we also demonstrate the convergence of these two data-driven algorithms under some mild conditions. Finally, we illustrate the practicality of our algorithms via two numerical examples.
title Two system transformation data-driven algorithms for linear quadratic mean-field games
topic Optimization and Control
url https://arxiv.org/abs/2404.10285