Improving the Bit Complexity of Communication for Distributed Convex Optimization
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910388638973952 |
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| author | Ghadiri, Mehrdad Lee, Yin Tat Padmanabhan, Swati Swartworth, William Woodruff, David Ye, Guanghao |
| author_facet | Ghadiri, Mehrdad Lee, Yin Tat Padmanabhan, Swati Swartworth, William Woodruff, David Ye, Guanghao |
| contents | 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 $1\leq p\leq 2$), 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improving the Bit Complexity of Communication for Distributed Convex Optimization Ghadiri, Mehrdad Lee, Yin Tat Padmanabhan, Swati Swartworth, William Woodruff, David Ye, Guanghao Data Structures and Algorithms Distributed, Parallel, and Cluster Computing Optimization and Control 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 $1\leq p\leq 2$), 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. |
| title | Improving the Bit Complexity of Communication for Distributed Convex Optimization |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing Optimization and Control |
| url | https://arxiv.org/abs/2403.19146 |