Global Convergence of Policy Gradient Algorithms for Indefinite Least Squares Stationary Optimal Control

Abstract

We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in control design with conflicting objectives, such as linear quadratic dynamic games. We show the global convergence of gradient, natural gradient and quasi-Newton policies for this class of indefinite least squares problems.