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Breaking the Nonsmooth Barrier: A Scalable Parallel Method for Composite Optimization

Fabian Pedregosa 1 Rémi Leblond 1 Simon Lacoste-Julien 2
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet, despite their practical success, support for nonsmooth objectives is still lacking, making them unsuitable for many problems of interest in machine learning, such as the Lasso, group Lasso or empirical risk minimization with convex constraints. In this work, we propose and analyze ProxASAGA, a fully asynchronous sparse method inspired by SAGA, a variance reduced incremental gradient algorithm. The proposed method is easy to implement and significantly outperforms the state of the art on several nonsmooth, large-scale problems. We prove that our method achieves a theoretical linear speedup with respect to the sequential version under assumptions on the sparsity of gradients and block-separability of the proximal term. Empirical benchmarks on a multi-core architecture illustrate practical speedups of up to 12x on a 20-core machine.
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https://hal.inria.fr/hal-01638058
Contributor : Fabian Pedregosa <>
Submitted on : Sunday, November 19, 2017 - 6:03:26 AM
Last modification on : Thursday, July 1, 2021 - 5:58:09 PM
Long-term archiving on: : Tuesday, February 20, 2018 - 12:29:38 PM

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  • HAL Id : hal-01638058, version 1
  • ARXIV : 1707.06468

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Fabian Pedregosa, Rémi Leblond, Simon Lacoste-Julien. Breaking the Nonsmooth Barrier: A Scalable Parallel Method for Composite Optimization. NIPS 2017 - Thirty-First Annual Conference on Neural Information Processing Systems, Dec 2017, Long Beach, United States. pp.1-28. ⟨hal-01638058⟩

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