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Mean-Field Neural Networks-Based Algorithms for McKean-Vlasov Control Problems

Year:    2024

Author:    Huyên Pham, Xavier Warin

Journal of Machine Learning, Vol. 3 (2024), Iss. 2 : pp. 176–214

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 [Pham and Warin, Neural Netw., 168, 2023] 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 stochastic differential equation 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.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jml.230106

Journal of Machine Learning, Vol. 3 (2024), Iss. 2 : pp. 176–214

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    39

Keywords:    Stochastic Gradient Descent Stochastic Stability Non-Convex Optimization Local Convergence Non-Isolated Minima. McKean-Vlasov control Mean-field neural networks Learning on Wasserstein space Dynamic programming Backward SDE.

Author Details

Huyên Pham

Xavier Warin

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