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We consider the classic stochastic linear quadratic regulator (LQR) problemunder an infinite horizon average stage cost. By leveraging recent policygradient methods from reinforcement learning, we obtain a first-order methodthat finds a stable feedback law whose objective function gap to the optima isat most $\varepsilon$ with high probability using $\tilde{O}(1/\varepsilon)$samples, where $\tilde{O}$ hides polylogarithmic dependence on $\varepsilon$.Our proposed method seems to have the best dependence on $\varepsilon$ withinthe model-free literature without the assumption that all policies generated bythe algorithm are stable almost surely, and it matches the best-known rate fromthe model-based literature, up to logarithmic factors. The improved dependenceon $\varepsilon$ is achieved by showing the accuracy scales with the variancerather than the standard deviation of the gradient estimation error. Ourdevelopments that result in this improved sampling complexity fall in thecategory of actor-critic algorithms. The actor part involves a variationalinequality formulation of the stochastic LQR problem, while in the critic part,we utilize a conditional stochastic primal-dual method and show that thealgorithm has the optimal rate of convergence when paired with a shrinkingmulti-epoch scheme.

A model-free first-order method for linear quadratic regulator with $\tilde{O}(1/\varepsilon)$ sampling complexity