Learning algorithms for mean field optimal control

2025/03/22 by Soner, H. Mete, Teichmann, Josef, Yan, Qinxin · 2 citations
#35D40 #35Q89 #49L25 #60G99 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.17869

Abstract

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an N-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein spaces.

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• Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators
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