Model-Free Linear Quadratic Regulator

Abstract

We review recent results on the convergence and sample complexity of the random search method for the infinite-horizon linear quadratic regulator (LQR) problem with unknown model parameters. This method directly searches over the space of stabilizing feedback gain matrices and, in spite of the lack of convexity, it converges to the globally optimal LQR solution at a linear rate. These results demonstrate that for a model-free method that utilizes two-point gradient estimates, the simulation time and the total number of function evaluations required for achieving ϵ -accuracy are both O(log(1/ϵ)).