Convergence of a robust deep FBSDE method for stochastic control
Journal article, 2023
from stochastic control. It is a modification of the deep BSDE method in which the initial value to the
backward equation is not a free parameter, and with a new loss function being the weighted sum of the cost
of the control problem, and a variance term which coincides with the mean squared error in the terminal
condition. We show by a numerical example that a direct extension of the classical deep BSDE method
to FBSDEs, fails for a simple linear-quadratic control problem, and motivate why the new method works.
Under regularity and boundedness assumptions on the exact controls of time continuous and time discrete
control problems, we provide an error analysis for our method. We show empirically that the method
converges for three different problems, one being the one that failed for a direct extension of the deep BSDE
method.
stochastic control
deep learning
FBSDE
Author
Kristoffer Andersson
Stichting Centrum voor Wiskunde & Informatica (CWI)
Adam Andersson
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Cornelis Oosterlee
Utrecht University
SIAM Journal of Scientific Computing
1064-8275 (ISSN) 1095-7197 (eISSN)
Vol. 45 1 A226-A255Subject Categories
Computational Mathematics
Control Engineering
Mathematical Analysis
DOI
10.1137/22M1478057