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arXiv · 2004.12210

Computational methods for nonlocal mean field games with applications

Siting Liu·Matthew Jacobs·Wuchen Li·Levon Nurbekyan·Stanley J. Osher
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Abstract

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. 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 (PDHG). We also discuss potential applications of our methods to multi-agent trajectory planning problems.

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Siting Liu, Matthew Jacobs, Wuchen Li, Levon Nurbekyan, Stanley J. Osher. 2020-04-25. Computational methods for nonlocal mean field games with applications. https://arxiv.org/abs/2004.12210

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