dc.contributor.author Kovalev, Dmitry dc.contributor.author Gasanov, Elnur dc.contributor.author Richtarik, Peter dc.contributor.author Gasnikov, Alexander dc.date.accessioned 2021-06-16T06:08:23Z dc.date.available 2021-06-16T06:08:23Z dc.date.issued 2021-06-08 dc.identifier.uri http://hdl.handle.net/10754/669593 dc.description.abstract We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network whose links are allowed to change in time. We solve two fundamental problems for this task. First, we establish the first lower bounds on the number of decentralized communication rounds and the number of local computations required to find an $\epsilon$-accurate solution. Second, we design two optimal algorithms that attain these lower bounds: (i) a variant of the recently proposed algorithm ADOM (Kovalev et al., 2021) enhanced via a multi-consensus subroutine, which is optimal in the case when access to the dual gradients is assumed, and (ii) a novel algorithm, called ADOM+, which is optimal in the case when access to the primal gradients is assumed. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2106.04469.pdf dc.rights Archived with thanks to arXiv dc.title Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks dc.type Preprint dc.contributor.department Computer Science dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Computer Science Program dc.eprint.version Pre-print dc.contributor.institution MIPT dc.identifier.arxivid 2106.04469 kaust.person Kovalev, Dmitry kaust.person Gasanov, Elnur kaust.person Richtarik, Peter refterms.dateFOA 2021-06-16T06:09:03Z
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