Approximate stochastic control based on deep learning and forward backward stochastic differential equations

Abstract

In this thesis numerical methods for stochastic optimal control are investigated. More precisely a nonlinear Gaussian diffusion type state equation with control in the drift and a quadratic cost functional with finite time horizon is considered. The proposed algorithm relies on recent work on deep learning based solvers for backward stochastic differential equations. The stochastic optimal control problem is reformulated as a forward backward stochastic differential equation and the algorithm is modified to apply to the problem of this thesis. The algorithm is tested on the benchmark problems of controlling single and double inverted pendulums on a cart. It is shown by numerical experiments that the algorithm performs well on both examples.