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Variance Reduced Stochastic Gradient Descent with Neighbors

Thomas Hofmann 1 Aurelien Lucchi 1 Simon Lacoste-Julien 2, 3, 4 Brian Mcwilliams 1
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence. However, these methods are either based on computations of full gradients at pivot points, or on keeping per data point corrections in memory. Therefore speed-ups relative to SGD may need a minimal number of epochs in order to materialize. This paper investigates algorithms that can exploit neighborhood structure in the training data to share and re-use information about past stochastic gradients across data points, which offers advantages in the transient optimization phase. As a side-product we provide a unified convergence analysis for a family of variance reduction algorithms, which we call memorization algorithms. We provide experimental results supporting our theory.
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Contributor : Simon Lacoste-Julien <>
Submitted on : Monday, December 28, 2015 - 4:30:01 AM
Last modification on : Tuesday, March 5, 2019 - 9:30:10 AM

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  • HAL Id : hal-01248672, version 1
  • ARXIV : 1506.03662



Thomas Hofmann, Aurelien Lucchi, Simon Lacoste-Julien, Brian Mcwilliams. Variance Reduced Stochastic Gradient Descent with Neighbors. NIPS 2015 - Advances in Neural Information Processing Systems 28, Dec 2015, Montreal, Canada. ⟨hal-01248672⟩



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