Mean-field neural networks-based algorithms for McKean-Vlasov control problems * - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Mean-field neural networks-based algorithms for McKean-Vlasov control problems *

Résumé

This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose several algorithms either based on dynamic programming with control learning by policy or value iteration, or backward SDE from stochastic maximum principle with global or local loss functions. Extensive numerical results on different examples are presented to illustrate the accuracy of each of our eight algorithms. We discuss and compare the pros and cons of all the tested methods.
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Dates et versions

hal-03900810 , version 1 (21-12-2022)
hal-03900810 , version 2 (18-03-2024)

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Huyên Pham, Xavier Warin. Mean-field neural networks-based algorithms for McKean-Vlasov control problems *. 2024. ⟨hal-03900810v2⟩
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