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Mathematics > Optimization and Control

arXiv:2210.00695 (math)
[Submitted on 3 Oct 2022]

Title:Automated Performance Estimation for Decentralized Optimization via Network Size Independent Problems

Authors:Sebastien Colla, Julien M. Hendrickx
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Abstract:We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case performance and worst-case instance of first-order optimization methods by solving an SDP. Unlike previous work, the size of our new PEP formulation is independent of the network size. For this purpose, we take a global view of the decentralized problem and we also decouple the consensus subspace and its orthogonal complement. We apply our methodology to different decentralized methods such as DGD, DIGing and EXTRA and obtain numerically tight performance guarantees that are valid for any network size.
Comments: 8 pages, 3 figures, accepted for Conference on Decision and Control 2022. arXiv admin note: text overlap with arXiv:2203.05963
Subjects: Optimization and Control (math.OC); Multiagent Systems (cs.MA)
Cite as: arXiv:2210.00695 [math.OC]
  (or arXiv:2210.00695v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.00695
Related DOI: https://doi.org/10.1109/CDC51059.2022.9993346

Submission history

From: Sebastien Colla [view email]
[v1] Mon, 3 Oct 2022 03:06:10 UTC (244 KB)
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