The convergence of sparsified gradient methods

conference paper The convergence of sparsified gradient methods published yes Dan-Adrian Alistarh author 4A899BFC-F248-11E8-B48F-1D18A9856A870000-0003-3650-940X Torsten Hoefler author Mikael Johansson author Nikola H Konstantinov author 4B9D76E4-F248-11E8-B48F-1D18A9856A87 Sarit Khirirat author Cedric Renggli author DaAl department ChLa department NeurIPS: Conference on Neural Information Processing Systems International IST Doctoral Program project 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. Neural Information Processing Systems Foundation2018Montreal, Canada eng Advances in Neural Information Processing Systems 31 1809.10505 000461852000047 Volume 20185973-5983 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 Foundation; 2018:5973-5983. 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, Dan-Adrian, et al. “The Convergence of Sparsified Gradient Methods.” Advances in Neural Information Processing Systems 31, vol. Volume 2018, Neural Information Processing Systems Foundation, 2018, pp. 5973–83. 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 Foundation, 2018. 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 Foundation. 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. 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 Foundation, 2018, pp. 5973–5983. 65892019-06-27T09:32:55Z2025-06-26T12:23:06Z