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

Author

Listed:
  • Huyên Pham

    (UPD7 - Université Paris Diderot - Paris 7, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Xavier Warin

    (EDF R&D - EDF R&D - EDF - EDF, FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF)

Abstract

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.

Suggested Citation

  • Huyên Pham & Xavier Warin, 2024. "Mean-field neural networks-based algorithms for McKean-Vlasov control problems ," Working Papers hal-03900810, HAL.
    • Handle: RePEc:hal:wpaper:hal-03900810
    Note: View the original document on HAL open archive server: https://hal.science/hal-03900810v2
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