Fast Policy Learning for Linear Quadratic Control with Entropy Regularization

TL;DR

This paper introduces two new policy learning algorithms, RPG and IPO, for entropy-regularized linear-quadratic control problems, demonstrating their convergence properties and effectiveness through theoretical analysis and numerical experiments.

Contribution

The paper develops and analyzes RPG and IPO algorithms with proven linear and super-linear convergence for entropy-regularized LQC, including transfer learning scenarios.

Findings

Both algorithms converge linearly to the optimal policy.

IPO achieves super-linear convergence near the optimum.

Numerical examples validate the algorithms' effectiveness.

Abstract

This paper proposes and analyzes two new policy learning methods: regularized policy gradient (RPG) and iterative policy optimization (IPO), for a class of discounted linear-quadratic control (LQC) problems over an infinite time horizon with entropy regularization. Assuming access to the exact policy evaluation, both proposed approaches are proven to converge linearly in finding optimal policies of the regularized LQC. Moreover, the IPO method can achieve a super-linear convergence rate once it enters a local region around the optimal policy. Finally, when the optimal policy for an RL problem with a known environment is appropriately transferred as the initial policy to an RL problem with an unknown environment, the IPO method is shown to enable a super-linear convergence rate if the two environments are sufficiently close. Performances of these proposed algorithms are supported by numerical examples.