Random features for high-dimensional nonlocal mean-field games

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. •Provide a novel framework to solve nonlocal high-dimensional mean field games.•The proposed framework is flexible and can use any trajectory generation/optimal control scheme.•Proposed framework is simple to program.