Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator

TL;DR

This paper proves that model-free policy gradient methods for linear quadratic regulators (LQR) globally converge to the optimal policy and are computationally and statistically efficient, bridging a theoretical gap in reinforcement learning.

Contribution

It establishes the global convergence and efficiency of policy gradient methods for LQR, providing theoretical guarantees previously lacking in continuous control.

Findings

Policy gradient methods globally converge for LQR.

They are polynomially efficient in sample and computational complexity.

The work bridges the gap between model-free RL and classical control theory.

Abstract

Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an "end-to-end" approach, directly optimizing the performance metric of interest 3) they inherently allow for richly parameterized policies. A notable drawback is that even in the most basic continuous control problem (that of linear quadratic regulators), these methods must solve a non-convex optimization problem, where little is understood about their efficiency from both computational and statistical perspectives. In contrast, system identification and model based planning in optimal control theory have a much more solid theoretical footing, where much is known with regards to their computational and statistical properties. This work bridges this gap showing that (model free) policy gradient methods globally converge to the optimal solution and are efficient (polynomially so in relevant problem dependent quantities) with regards to their sample and computational complexities.