Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control
Numerical Analysis
2021-08-03 v5 Numerical Analysis
Machine Learning
Abstract
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.
Cite
@article{arxiv.1712.04667,
title = {Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control},
author = {D. Belomestny and L. Iosipoi and Q. Paris and N. Zhivotovskiy},
journal= {arXiv preprint arXiv:1712.04667},
year = {2021}
}
Comments
32 pages, to appear in Bernoulli