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
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