Random Features for High-Dimensional Nonlocal Mean-Field Games

TL;DR

This paper introduces a Monte Carlo-based random feature method to efficiently solve high-dimensional nonlocal mean-field game systems, bypassing costly discretizations and extending single-agent algorithms to the mean-field context.

Contribution

It presents a novel approach using random features for high-dimensional MFGs, enabling solutions where traditional methods are computationally infeasible.

Findings

Successfully solves high-dimensional MFG problems previously out of reach.

Demonstrates efficiency and scalability of the random feature approach.

Extends single-agent trajectory optimization to the mean-field setting.

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.