Deep Learning Methods for Mean Field Control Problems With Delay

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 parameterize the optimal control using neural networks, the other is ba...

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Bibliographic Details
Published in:Frontiers in applied mathematics and statistics Vol. 6
Main Authors: Fouque, Jean-Pierre, Zhang, Zhaoyu
Format: Journal Article
Language:English
Published: Frontiers Media S.A 12-05-2020
Subjects:
deep learning
delay
McKean-Vlasov
mean field control
stochastic maximum principal
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Summary: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 parameterize 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 existence and uniqueness results are proved for the associated MV-FABSDE system under suitable conditions.Mathematical Subject Classification (2000): 93E20, 60G99, 68-04
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2020.00011