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Title: Deep Learning Methods for Mean Field Control Problems with Delay
We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly parameterizing the optimal control using neural networks, the other is based on numerically solving the McKean-Vlasov forward anticipated backward stochastic differential equation (MV-FABSDE) system. In addition, we establish the necessary and sufficient stochastic maximum principle of this class of mean field control problems with delay based on the differential calculus on function of measures, and the exis- tence and uniqueness results are proved for the associated MV-FABSDE system under suitable conditions.  more » « less
Award ID(s):
1814091
PAR ID:
10335531
Author(s) / Creator(s):
Date Published:
Journal Name:
Frontiers in applied mathematics and statistics
Volume:
6
Issue:
11
ISSN:
2297-4687
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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