Random Features for High-Dimensional Nonlocal Mean-Field Games
arXiv:2202.12529 · doi:10.1016/j.jcp.2022.111136
Abstract
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.
arXiv comment27 pages
References in corpus (9)
- A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems
- Game theoretic modelling of infectious disease dynamics and intervention methods: a mini-review
- A Mean-Field Optimal Control Formulation of Deep Learning
- Finite mean field games: fictitious play and convergence to a first order continuous mean field game
- Maximum principles at infinity and the Ahlfors-Khas'minskii duality: an overview
- A Neural Network Approach Applied to Multi-Agent Optimal Control
- Numerical methods for Mean field Games based on Gaussian Processes and Fourier Features
- A mean-field game approach to price formation in electricity markets
- A Simple Multiscale Method for Mean Field Games