Deep Learning Methods for Mean Field Control Problems With Delay

被引：30

作者：

Fouque, Jean-Pierre ^{[1
]}

Zhang, Zhaoyu ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93106 USA

来源：

FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS | 2020年 / 6卷

关键词：

deep learning; mean field control; delay; McKean-Vlasov; stochastic maximum principal; STOCHASTIC DIFFERENTIAL-EQUATIONS; GAMES;

D O I：

10.3389/fams.2020.00011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页数：17