Deep Learning Methods for Mean Field Control Problems With Delay
Deep Learning Methods for Mean Field Control Problems With Delay
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DOI：
10.3389/fams.2020.00011
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
J. Fouque;Zhao-qin Zhang
中科院分区：
文献类型：
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作者：
J. Fouque;Zhao-qin Zhang
我们考虑一类由McKean-Vlasov型随机时滞微分方程描述的一般平均场控制问题。给出了两种基于深度学习技术的数值算法，一种是利用神经网络直接对最优控制进行参数化，另一种是基于数值求解McKean-Vlasov正向预期倒向随机微分方程(MV-FABSDE)系统。此外，基于关于测度函数的微积分，我们建立了这类时滞平均场控制问题的充要随机极大值原理，并在适当的条件下证明了相关MV-FABSDE系统解的存在唯一性。数学学科分类(2000)：93E20、60G99、68-04
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