Sega: Variance reduction via gradient sketching

Filip Hanzely, Konstantin Mishchenko, Peter Richtárik

Research output: Contribution to conferencePaperpeer-review

31 Scopus citations

Abstract

We propose a randomized first order optimization method-SEGA (SkEtched GrAdient)-which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the gradient. In each iteration, SEGA updates the current estimate of the gradient through a sketch-and-project operation using the information provided by the latest sketch, and this is subsequently used to compute an unbiased estimate of the true gradient through a random relaxation procedure. This unbiased estimate is then used to perform a gradient step. Unlike standard subspace descent methods, such as coordinate descent, SEGA can be used for optimization problems with a non-separable proximal term. We provide a general convergence analysis and prove linear convergence for strongly convex objectives. In the special case of coordinate sketches, SEGA can be enhanced with various techniques such as importance sampling, minibatching and acceleration, and its rate is up to a small constant factor identical to the best-known rate of coordinate descent.

Original languageEnglish (US)
Pages2082-2093
Number of pages12
StatePublished - 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

Conference

Conference32nd Conference on Neural Information Processing Systems, NeurIPS 2018
Country/TerritoryCanada
CityMontreal
Period12/2/1812/8/18

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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