# Empirical Variance Minimization with Applications in Variance Reduction and Optimal Control

arXiv: https://arxiv.org/abs/1712.04667 · HTML: https://mlsanity.com/paper/1712.04667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2017.

## Built on by (most cited first, 3 of 3)

- [Variance Reduction for Policy-Gradient Methods via Empirical Variance Minimization](https://mlsanity.com/paper/2206.06827/) (2022)
- [Theoretical guarantees for neural control variates in MCMC](https://mlsanity.com/paper/2304.01111/) (2023)
- [A Quadrature Rule combining Control Variates and Adaptive Importance Sampling](https://mlsanity.com/paper/2205.11890/) (2022)

## Abstract (arXiv)

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.