Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method

TL;DR

This paper introduces a reinforcement learning approach for solving infinite horizon stochastic linear quadratic control problems, enabling direct computation of optimal control with minimal system information and no need for Riccati equation solutions.

Contribution

The paper presents a novel RL algorithm that directly finds optimal controls in stochastic LQ problems using only local trajectory data, bypassing traditional Riccati equation methods.

Findings

The RL method successfully computes optimal controls in numerical examples.

The approach simplifies calculations by avoiding explicit system coefficient estimation.

The algorithm operates with partial system information, demonstrating practical applicability.

Abstract

This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on Bellman's dynamic programming principle, an online RL algorithm is presented to attain the optimal control with just partial system information. This algorithm directly computes the optimal control rather than estimating the system coefficients and solving the related Riccati equation. It just requires local trajectory information, greatly simplifying the calculation processing. Two numerical examples are carried out to shed light on our theoretical findings.