(Cheap) Stochastic Policy Gradient Converges with High Probability for Linear Quadratic Regulator

Abstract

We study the convergence of the vanilla stochastic policy gradient method applied to the linear quadratic regulator (LQR) problem. The method is cheap in the following sense: (1) at each iteration only $\tilde{O}(1)$ interactions with the environment are needed, therefore allowing frequent policy improvement steps, and (2) to ensure stability throughout and convergence to an $\epsilon$-optimal policy with probability $1-\delta$, only $O(\mathtt{Polylog}(1/\delta )/\epsilon )$ interactions are needed. To the best of our knowledge, this appears to be the first time that a stochastic model-free policy optimization method for LQR converges with high probability with $\tilde{O}(1)$ per-iteration computation and polylogarithmic dependence on the confidence level. The convergence analysis presented here is agnostic to LQR specifics and hence could be potentially generalized to a broader class of problems.