2016

A Simple Practical Accelerated Method for Finite Sums

Defazio, Aaron

Understand

We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method.

  • Our method achieves an accelerated convergence rate on strongly convex smooth problems.
  • Our method has only one parameter (a step size), and is radically simpler than other accelerated methods for finite sums.
  • Additionally it can be applied when the terms are non-smooth, yielding a method applicable in many areas where operator splitting methods would traditionally be applied.

Built on

  • Monotone operators and the proximal point algorithm

    R Tyrrell Rockafellar · 1976

    Earlier work this paper cites.

  • Introductory Lectures On Convex Programming

    Yu. Nesterov · 1998

    Earlier work this paper cites.

  • Libsvm : a library for support vector machines

    Chih-Chung Chang and Chih-Jen Lin · 2011

    Earlier work this paper cites.

  • Pegasos: Primal estimated sub-gradient solver for svm

    Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, and Andrew Cotter · 2011

    Earlier work this paper cites.

  • Accelerating stochastic gradient descent using predictive variance reduction

    Rie Johnson and Tong Zhang · 2013

    Earlier work this paper cites.

Similar

  • Semi-Stochastic Gradient Descent Methods

    Jakub Konečný and Peter Richtárik · 2013

    Cited alongside, same era.

  • Minimizing finite sums with the stochastic average gradient

    Mark Schmidt, Nicolas Le Roux, and Francis Bach · 2013

    Cited alongside, same era.

  • Saga: A fast incremental gradient method with support for non-strongly convex composite objectives

    Aaron Defazio, Francis Bach, and Simon Lacoste-Julien · 2014

    Cited alongside, same era.

  • Incremental majorization-minimization optimization with application to large-scale machine learning

    Julien Mairal · 2014

    Cited alongside, same era.

  • Finito: A faster, permutable incremental gradient method for big data problems

    Aaron Defazio, Tiberio Caetano, and Justin Domke

    Cited in the paper.

  • Stochastic dual coordinate ascent methods for regularized loss minimization

    Shai Shalev-Shwartz and Tong Zhang

    Cited in the paper.

  • Accelerated mini-batch stochastic dual coordinate ascent

    Shai Shalev-Shwartz and Tong Zhang

    Cited in the paper.

  • Accelerated proximal stochastic dual coordinate ascent for regularized loss minimization

    Shai Shalev-Shwartz and Tong Zhang

    Cited in the paper.

Then

  • Stochastic proximal gradient descent with acceleration techniques

    Atsushi Nitanda · 2014

    Later among the works it cites.

  • Variance reduced stochastic gradient descent with neighbors

    Thomas Hofmann, Aurelien Lucchi, Simon Lacoste-Julien, and Brian McWilliams · 2015

    Later among the works it cites.

  • An optimal randomized incremental gradient method

    G. Lan and Y. Zhou · 2015

    Later among the works it cites.

  • A universal catalyst for first-order optimization

    Hongzhou Lin, Julien Mairal, and Zaid Harchaoui · 2015

    Later among the works it cites.

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