An Effective Discrete Recursive Method for Stochastic Optimal Control Problems

TL;DR

This paper introduces a discrete recursive method for solving stochastic optimal control problems, leveraging a new stochastic maximum principle, with proven first-order convergence and supporting numerical experiments.

Contribution

It presents a novel discrete recursive approach for SOCPs based on a newly derived stochastic maximum principle, with rigorous error analysis.

Findings

The method achieves first-order convergence in cost.

Numerical experiments validate theoretical error bounds.

The approach effectively handles feedback control in stochastic settings.

Abstract

In this paper, we study the numerical method for stochastic optimal control problems (SOCPs). By reducing the optimal control problem to the discrete case, we derive a discrete stochastic maximum principle (SMP). With the help of this SMP, we propose an effective discrete recursive method for SOCPs with feedback control. We rigorously analyze errors of the proposed method and prove that the cost obtained by our method is of first-order convergence. Numerical experiments are carried out to support our theoretical results.