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The Convergence of Sparsified Gradient Methods
IST Austria, Klosterneuburg, Austria..
Swiss Fed Inst Technol, Zurich, Switzerland..
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.ORCID iD: 0000-0003-4473-2011
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2018 (English)In: Advances in Neural Information Processing Systems 31 (NIPS 2018) / [ed] Bengio, S Wallach, H Larochelle, H Grauman, K CesaBianchi, N Garnett, R, Neural Information Processing Systems (NIPS) , 2018, Vol. 31Conference paper, Published paper (Refereed)
Abstract [en]

Stochastic Gradient Descent (SGD) has become the standard tool for distributed training of massive machine learning models, in particular deep neural networks. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed to reduce the overheads of distribution. To date, gradient sparsification methods-where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally-are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to three orders of magnitude, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis also reveals that these methods do require analytical conditions to converge well, justifying and complementing existing heuristics.

Place, publisher, year, edition, pages
Neural Information Processing Systems (NIPS) , 2018. Vol. 31
Series
Advances in Neural Information Processing Systems, ISSN 1049-5258 ; 31
National Category
Other Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-249918ISI: 000461852000047Scopus ID: 2-s2.0-85064812369OAI: oai:DiVA.org:kth-249918DiVA, id: diva2:1307203
Conference
32nd Conference on Neural Information Processing Systems (NIPS), DEC 02-08, 2018, Montreal, Canada
Note

QC 20190426

Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-10-09Bibliographically approved

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Johansson, MikaelKhirirat, Sarit

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