Accelerated Optimization of the Linear-Quadratic Regulator Problem

This paper introduces an accelerated optimization framework for solving the linear-quadratic regulator (LQR) problem, which is a landmark problem in optimal control. The authors present novel continuous-time and discrete-time algorithms that achieve Nesterov-optimal convergence rates for the state-feedback LQR (SLQR) problem. For the output-feedback LQR (OLQR) problem, a Hessian-free accelerated framework is proposed that can find an ϵ-stationary point with second-order guarantee in a time of O(ϵ^(-7/4) log(1/ϵ)).