Policy gradient methods for discrete time linear quadratic regulator with random parameters

Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, PR China

^* Corresponding author: lidy21@m.fudan.edu.cn

Received: 29 March 2023
Accepted: 27 February 2024

Abstract

This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general setting, we apply the policy gradient method, a reinforcement learning technique, to search for the optimal control without requiring knowledge of statistical information of the parameters. We investigate the sub-Gaussianity of the state process and establish global linear convergence guarantee for this approach based on assumptions that are weaker and easier to verify compared to existing results. Numerical experiments are presented to illustrate our result.