Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control
This work addresses variance reduction and optimal control problems, providing theoretical guarantees for practitioners in these domains.
The paper tackles the problem of empirical minimization for variance-type functionals, deriving sharp non-asymptotic bounds for excess variance and showing that fast convergence rates, including optimal non-parametric rates, can be achieved under certain conditions on the functional class.
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved including the optimal non-parametric rates for expressive classes in the non-Donsker regime under some additional assumptions. Our main applications include variance reduction and optimal control.