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arXiv · 2010.00892

Variance-Reduced Methods for Machine Learning

Robert M. Gower·Mark Schmidt·Francis Bach·Peter Richtarik
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Abstract

Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago. The last 8 years have seen an exciting new development: variance reduction (VR) for stochastic optimization methods. These VR methods excel in settings where more than one pass through the training data is allowed, achieving a faster convergence than SGD in theory as well as practice. These speedups underline the surge of interest in VR methods and the fast-growing body of work on this topic. This review covers the key principles and main developments behind VR methods for optimization with finite data sets and is aimed at non-expert readers. We focus mainly on the convex setting, and leave pointers to readers interested in extensions for minimizing non-convex functions.

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BibTeXRIS

Robert M. Gower, Mark Schmidt, Francis Bach, Peter Richtarik. 2020-10-02. Variance-Reduced Methods for Machine Learning. https://arxiv.org/abs/2010.00892

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