The convergence of sparsified gradient methods

D.-A. Alistarh, T. Hoefler, M. Johansson, N.H. Konstantinov, S. Khirirat, C. Renggli, in:, Advances in Neural Information Processing Systems 31, Neural information processing systems, 2018, pp. 5973–5983.

Conference Paper | Published | English
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Abstract
Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed. 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 \emph{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 and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.
Publishing Year
Date Published
2018-12-01
Proceedings Title
Advances in Neural Information Processing Systems 31
Volume
Volume 2018
Page
5973-5983
Conference
NeurIPS: Conference on Neural Information Processing Systems
Conference Location
Montreal, Canada
Conference Date
2018-12-02 – 2018-12-08
IST-REx-ID

Cite this

Alistarh D-A, Hoefler T, Johansson M, Konstantinov NH, Khirirat S, Renggli C. The convergence of sparsified gradient methods. In: Advances in Neural Information Processing Systems 31. Vol Volume 2018. Neural information processing systems; 2018:5973-5983.
Alistarh, D.-A., Hoefler, T., Johansson, M., Konstantinov, N. H., Khirirat, S., & Renggli, C. (2018). The convergence of sparsified gradient methods. In Advances in Neural Information Processing Systems 31 (Vol. Volume 2018, pp. 5973–5983). Montreal, Canada: Neural information processing systems.
Alistarh, Dan-Adrian, Torsten Hoefler, Mikael Johansson, Nikola H Konstantinov, Sarit Khirirat, and Cedric Renggli. “The Convergence of Sparsified Gradient Methods.” In Advances in Neural Information Processing Systems 31, Volume 2018:5973–83. Neural information processing systems, 2018.
D.-A. Alistarh, T. Hoefler, M. Johansson, N. H. Konstantinov, S. Khirirat, and C. Renggli, “The convergence of sparsified gradient methods,” in Advances in Neural Information Processing Systems 31, Montreal, Canada, 2018, vol. Volume 2018, pp. 5973–5983.
Alistarh D-A, Hoefler T, Johansson M, Konstantinov NH, Khirirat S, Renggli C. 2018. The convergence of sparsified gradient methods. Advances in Neural Information Processing Systems 31. NeurIPS: Conference on Neural Information Processing Systems vol. Volume 2018. 5973–5983.
Alistarh, Dan-Adrian, et al. “The Convergence of Sparsified Gradient Methods.” Advances in Neural Information Processing Systems 31, vol. Volume 2018, Neural information processing systems, 2018, pp. 5973–83.

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