Online Variance Reduction for Stochastic Optimization

TL;DR

This paper introduces an online variance reduction algorithm for stochastic optimization that adaptively learns importance sampling distributions, improving convergence by reducing variance in data estimates.

Contribution

It presents the first online algorithm for variance reduction via importance sampling that competes with the best fixed distribution in hindsight.

Findings

Algorithm effectively reduces variance in stochastic estimates.

Empirical results show improved convergence in various settings.

Abstract

Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible remedy is to employ non-uniform importance sampling techniques, which take the structure of the dataset into account. In this work, we investigate a recently proposed setting which poses variance reduction as an online optimization problem with bandit feedback. We devise a novel and efficient algorithm for this setting that finds a sequence of importance sampling distributions competitive with the best fixed distribution in hindsight, the first result of this kind. While we present our method for sampling datapoints, it naturally extends to selecting coordinates or even blocks of thereof. Empirical validations underline the benefits of our method in several settings.