TY - JOUR
T1 - A Stochastic Gradient Descent Approach for Stochastic Optimal Control
AU - Archibald , Richard
AU - Bao , Feng
AU - Yong , Jiongmin
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 - <p style="text-align: justify;">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.</p>