Scalable Method for Mean Field Control with Kernel Interactions via Random Fourier Features

TL;DR

This paper introduces a scalable algorithm for mean field control with kernel interactions, using random Fourier features to reduce computational complexity and enable efficient training of feedback controls in large populations.

Contribution

It combines particle simulations with random Fourier features to replace quadratic kernel evaluations, providing a practical and efficient approach for large-scale mean field control problems.

Findings

Reduces computational cost significantly

Maintains control performance in large populations

Effective in high-dimensional scenarios

Abstract

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by linear-time estimates, enabling efficient stochastic gradient descent for training feedback controls in large populations. We provide theoretical complexity bounds and demonstrate through crowd motion and flocking examples that the approach preserves control performance while substantially reducing computational cost. The results indicate that random feature approximations offer an effective and practical tool for high dimensional and large scale mean field control.