Accelerating Variance-Reduced Stochastic Gradient Methods

Derek Driggs, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticle

Abstract

Variance reduction is a crucial tool for improving the slow convergence of stochastic gradient descent. Only a few variance-reduced methods, however, have yet been shown to directly benefit from Nesterov’s acceleration techniques to match the convergence rates of accelerated gradient methods. Such approaches rely on “negative momentum”, a technique for further variance reduction that is generally specific to the SVRG gradient estimator. In this work, we show for the first time that negative momentum is unnecessary for acceleration and develop a universal acceleration framework that allows all popular variance-reduced methods to achieve accelerated convergence rates. The constants appearing in these rates, including their dependence on the number of functions n, scale with the mean-squared-error and bias of the gradient estimator. In a series of numerical experiments, we demonstrate that versions of SAGA, SVRG, SARAH, and SARGE using our framework significantly outperform non-accelerated versions and compare favourably with algorithms using negative momentum.

Original languageEnglish
JournalMathematical Programming
Early online date15 Sep 2020
DOIs
Publication statusE-pub ahead of print - 15 Sep 2020

Keywords

  • Accelerated gradient descent
  • Convex optimisation
  • Stochastic optimisation
  • Variance reduction

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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