TY - JOUR
T1 - Mean-Field Neural Networks-Based Algorithms for McKean-Vlasov Control Problems
AU - Pham , Huyên
AU - Warin , Xavier
JO - Journal of Machine Learning
VL - 2
SP - 176
EP - 214
PY - 2024
DA - 2024/06
SN - 3
DO - http://doi.org/10.4208/jml.230106
UR - https://global-sci.org/intro/article_detail/jml/23211.html
KW - McKean-Vlasov control, Mean-field neural networks, Learning on Wasserstein space, Dynamic programming, Backward SDE.
AB - <p style="text-align: justify;">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.</p>