Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control

Understand

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.