Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems
This work addresses policy optimization for control systems, providing theoretical guarantees for derivative-free methods, but it is incremental as it focuses on specific linear-quadratic settings.
The paper tackles the problem of optimizing linear policies in linear-quadratic systems using derivative-free methods, showing that these methods converge to near-optimal policies with a polynomial number of evaluations in terms of error tolerance, dimension, and curvature.
We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback. We show that these methods provably converge to within any pre-specified tolerance of the optimal policy with a number of zero-order evaluations that is an explicit polynomial of the error tolerance, dimension, and curvature properties of the problem. Our analysis reveals some interesting differences between the settings of additive driving noise and random initialization, as well as the settings of one-point and two-point reward feedback. Our theory is corroborated by extensive simulations of derivative-free methods on these systems. Along the way, we derive convergence rates for stochastic zero-order optimization algorithms when applied to a certain class of non-convex problems.