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A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets

Nicolas Le Roux 1, 2, * Mark Schmidt 1, 2 Francis Bach 1, 2
* Corresponding author
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard algorithms, both in terms of optimizing the training error and reducing the test error quickly.
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https://hal.inria.fr/hal-00674995
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Submitted on : Monday, March 11, 2013 - 4:47:10 PM
Last modification on : Thursday, July 1, 2021 - 5:58:07 PM
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  • HAL Id : hal-00674995, version 4
  • ARXIV : 1202.6258

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Nicolas Le Roux, Mark Schmidt, Francis Bach. A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets. NIPS'12 - 26 th Annual Conference on Neural Information Processing Systems (2012), 2012, Lake Tahoe, United States. ⟨hal-00674995v4⟩

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