Year: 2020
Author: Richard Archibald, Feng Bao, Jiongmin Yong
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 635–658
Abstract
In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. The motivation that drives our method is the gradient of the cost functional in the stochastic optimal control problem is under expectation, and numerical calculation of such an expectation requires fully computation of a system of forward backward stochastic differential equations, which is computationally expensive. By evaluating the expectation with single-sample representation as suggested by the stochastic gradient descent type optimisation, we could save computational efforts in solving FBSDEs and only focus on the optimisation task which aims to determine the optimal control process.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.190420.200420
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 635–658
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Stochastic optimal control stochastic gradient descent maximum principle forward backward stochastic differential equations.