Mini-Batch Semi-Stochastic Gradient Descent in the Proximal Setting

Jakub Konečný, Jie Liu, Peter Richtárik, Martin Takáč

Research output: Contribution to journalArticlepeer-review

104 Scopus citations

Abstract

We propose mS2GD: a method incorporating a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent (S2GD). We consider the problem of minimizing a strongly convex function represented as the sum of an average of a large number of smooth convex functions, and a simple nonsmooth convex regularizer. Our method first performs a deterministic step (computation of the gradient of the objective function at the starting point), followed by a large number of stochastic steps. The process is repeated a few times with the last iterate becoming the new starting point. The novelty of our method is in introduction of mini-batching into the computation of stochastic steps. In each step, instead of choosing a single function, we sample b functions, compute their gradients, and compute the direction based on this. We analyze the complexity of the method and show that it benefits from two speedup effects. First, we prove that as long as b is below a certain threshold, we can reach any predefined accuracy with less overall work than without mini-batching. Second, our mini-batching scheme admits a simple parallel implementation, and hence is suitable for further acceleration by parallelization.

Original languageEnglish (US)
Article number7347336
Pages (from-to)242-255
Number of pages14
JournalIEEE Journal on Selected Topics in Signal Processing
Volume10
Issue number2
DOIs
StatePublished - Mar 2016

Keywords

  • Empirical risk minimization
  • mini-batches
  • proximal methods
  • semi-stochastic gradient descent
  • sparse data
  • stochastic gradient descent
  • variance reduction

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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