COMPUTATIONAL METHODS FOR FIRST-ORDER NONLOCAL MEAN FIELD GAMES WITH APPLICATIONS.
- Resource Type
- Article
- Authors
- LIU, SITING; JACOBS, MATTHEW; WUCHEN LI; NURBEKYAN, LEVON; OSHER, STANLEY J.
- Source
- SIAM Journal on Numerical Analysis. 2021, Vol. 59 Issue 5, p2639-2668. 30p.
- Subject
- *MACHINE learning
*MEAN field theory
*GAMES
*KERNEL (Mathematics)
*SEPARATION of variables
*MACHINE theory
- Language
- ISSN
- 0036-1429
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. [ABSTRACT FROM AUTHOR]