Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control

In this paper we propose and study a generic variance reduction approach. The proposed method is based on minimization of the empirical variance over a suitable class of zero mean control functionals. We discuss several possibilities of constructing zero mean control functionals and present non-asymptotic error bounds for the variance reduced Monte Carlo estimates. Finally, a simulation study showing numerical efficiency of the proposed approach is presented.