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Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus

Azizan-Ruhi, Navid and Lahouti, Farshad and Avestimehr, Salman and Hassibi, Babak (2019) Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus. IEEE Transactions on Signal Processing, 67 (14). pp. 3806-3817. ISSN 1053-587X. doi:10.1109/TSP.2019.2917855.

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Solving a large-scale system of linear equations is a key step at the heart of many algorithms in scientific computing, machine learning, and beyond. When the problem dimension is large, computational and/or memory constraints make it desirable, or even necessary, to perform the task in a distributed fashion. In this paper, we consider a common scenario in which a taskmaster intends to solve a large-scale system of linear equations by distributing subsets of the equations among a number of computing machines/cores. We propose a new algorithm called Accelerated Projection-based Consensus , in which at each iteration every machine updates its solution by adding a scaled version of the projection of an error signal onto the nullspace of its system of equations, and the taskmaster conducts an averaging over the solutions with momentum. The convergence behavior of the proposed algorithm is analyzed in detail and analytically shown to compare favorably with the convergence rate of alternative distributed methods, namely distributed gradient descent, distributed versions of Nesterov's accelerated gradient descent and heavy-ball method, the block Cimmino method, and Alternating Direction Method of Multipliers. On randomly chosen linear systems, as well as on real-world data sets, the proposed method offers significant speed-up relative to all the aforementioned methods. Finally, our analysis suggests a novel variation of the distributed heavy-ball method, which employs a particular distributed preconditioning and achieves the same theoretical convergence rate as that in the proposed consensus-based method.

Item Type:Article
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URLURL TypeDescription Paper ItemConference Paper
Azizan-Ruhi, Navid0000-0002-4299-2963
Lahouti, Farshad0000-0002-8729-873X
Additional Information:© 2019 IEEE. Manuscript received June 25, 2018; revised December 14, 2018 and April 2, 2019; accepted April 26, 2019. Date of publication June 4, 2019; date of current version June 21, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Laura Cottatellucci. This work was supported in part by the National Science Foundation under Grants CCF-1423663, CCF-1409204, and ECCS-1509977, in part by a grant from Qualcomm Inc., in part by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and in part by fellowships from Amazon Web Services, Inc., and PIMCO, LLC. This paper was presented in part at the IEEE International Conference on Acoustics, Speech, and Signal Processing, Calgary, AB, Canada, April 2018.
Funding AgencyGrant Number
JPL President and Director's FundUNSPECIFIED
Amazon Web ServicesUNSPECIFIED
Subject Keywords:System of linear equations, distributed computing, big data, consensus, optimization
Issue or Number:14
Record Number:CaltechAUTHORS:20190610-092256233
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Official Citation:N. Azizan-Ruhi, F. Lahouti, A. S. Avestimehr and B. Hassibi, "Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus," in IEEE Transactions on Signal Processing, vol. 67, no. 14, pp. 3806-3817, 15 July, 2019. doi: 10.1109/TSP.2019.2917855
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96231
Deposited By: Tony Diaz
Deposited On:10 Jun 2019 17:08
Last Modified:16 Nov 2021 17:19

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