Volume 10, Issue 4
A Stochastic Gradient Descent Approach for Stochastic Optimal Control

Richard Archibald, Feng Bao & Jiongmin Yong

East Asian J. Appl. Math., 10 (2020), pp. 635-658.

Published online: 2020-08

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  • 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.

  • Keywords

Stochastic optimal control, stochastic gradient descent, maximum principle, forward backward stochastic differential equations.

  • AMS Subject Headings

65K10, 49M37, 49M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-635, author = {Richard Archibald , and Feng Bao , and Jiongmin Yong , }, title = {A Stochastic Gradient Descent Approach for Stochastic Optimal Control}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190420.200420}, url = {http://global-sci.org/intro/article_detail/eajam/17944.html} }
TY - JOUR T1 - A Stochastic Gradient Descent Approach for Stochastic Optimal Control AU - Richard Archibald , AU - Feng Bao , AU - Jiongmin Yong , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 635 EP - 658 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.190420.200420 UR - https://global-sci.org/intro/article_detail/eajam/17944.html KW - Stochastic optimal control, stochastic gradient descent, maximum principle, forward backward stochastic differential equations. AB -

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.

Richard Archibald, Feng Bao & Jiongmin Yong. (2020). A Stochastic Gradient Descent Approach for Stochastic Optimal Control. East Asian Journal on Applied Mathematics. 10 (4). 635-658. doi:10.4208/eajam.190420.200420
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