Improving the Bit Complexity of Communication for Distributed Convex Optimization
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3618260.3649787.pdf
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Author(s)
Ghadiri, Mehrdad
Lee, Yin Tat
Padmanabhan, Swati
Swartworth, William
Woodruff, David P.
Ye, Guanghao
Date Issued
June 10, 2024
Publisher
ACM|Proceedings of the 56th Annual ACM Symposium on Theory of Computing
Citation
Ghadiri, Mehrdad, Lee, Yin Tat, Padmanabhan, Swati, Swartworth, William, Woodruff, David P. et al. 2024. "Improving the Bit Complexity of Communication for Distributed Convex Optimization."
Version
Final published version
Abstract
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, p-norm regression (for 1≤ p≤ 2), linear programming, minimizing the sum of finitely many convex nonsmooth functions with varying supports, and low rank approximation; for a number of these fundamental problems our bounds are nearly optimal, as proven by our lower bounds. Among our techniques, we use the notion of block leverage scores, which have been relatively unexplored in this context, as well as dropping all but the “middle” bits in Richardson-style algorithms. We also introduce a new communication problem for accurately approximating inner products and establish a lower bound using the spherical Radon transform. Our lower bound can be used to show the first separation of linear programming and linear systems in the distributed model when the number of constraints is polynomial, addressing an open question in prior work.
Description
STOC ’24, June 24–28, 2024, Vancouver, BC, Canada
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Operations Research Center
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Creative Commons Attribution-Noncommercial-ShareAlike
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DOI of Published Version
https://doi.org/10.1145/3618260.3649787
