  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.
