Random features for high-dimensional nonlocal mean-field games. (English) Zbl 07525128

Summary: 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.


91Axx Game theory
35Qxx Partial differential equations of mathematical physics and other areas of application
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems


OT-Flow; Julia
Full Text: DOI


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