Random Features for High-Dimensional Nonlocal Mean-Field Games

Autor:	Agrawal, Sudhanshu, Lee, Wonjun, Fung, Samy Wu, Nurbekyan, Levon
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis Mathematics - Optimization and Control
Zdroj:	J. Comput. Phys., 459(C), jun 2022
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jcp.2022.111136
Popis:	We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction terms in the state-space by passing to the feature-space. This approach allows for a seamless mean-field extension of virtually any single-agent trajectory optimization algorithm. Here, we extend the direct transcription approach in optimal control to the mean-field setting. We demonstrate the efficiency of our method by solving MFG problems in high-dimensional spaces which were previously out of reach for conventional non-deep-learning techniques. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.12529 Zobrazit plný text záznamu View this record from Arxiv