期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 59, 期 5, 页码 2639-2668出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1334668
关键词
mean field games; kernel methods; multiagent systems; optimal control; Fourier methods
资金
- AFOSR MURI [FA9550-18-1-0502]
- AFOSR [FA9550-18-1-0167]
- ONR [N00014-18-1-2527, N00014-20-1-2093]
- Simons Foundation
- Centre de Recherches Mathematiques through the Simons-CRM scholar-in-residence program
This study presents a novel framework for modeling and solving first-order mean field game systems with nonlocal interactions, demonstrating flexibility and efficiency for potential applications in multiagent trajectory planning problems.
We introduce a novel framework to model and solve first-order mean field game systems with nonlocal interactions, extending the results in [L. Nurbekyan and J. Saude, Port. Math., 75 (2018), pp. 367-396]. Our approach relies on kernel-based representations of mean field interactions and feature-space expansions in the spirit of kernel methods in machine learning. We demonstrate the flexibility of our approach by modeling various interaction scenarios between agents. Additionally, our method yields a computationally efficient saddle-point reformulation of the original problem that is amenable to state-of-the-art convex optimization methods such as the primal-dual hybrid gradient method. We also discuss potential applications of our methods to multiagent trajectory planning problems.
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