Global Convergence of Policy Gradient Methods for Linearized Control Problems

Maryam Fazel, Rong Ge, Sham M. Kakade, Mehran Mesbahi

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.

TL;DR: This paper shows that model-free policy gradient methods can converge to the global optimal solution for non-convex linearized control problems.

Keywords: linear quadratic regulator, policy gradient, natural gradient, reinforcement learning, non-convex optimization