Optimal distributed convex optimization on slowly time-varying graphs

Alexander Rogozin, Cesar A. Uribe, Alexander V. Gasnikov, Nikolay Malkovsky, Angelia Nedic

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up to logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Ω (equation presented) for decentralized algorithms, where κΦ is the condition number of the objective function, and χ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.

Original languageEnglish (US)
Article number8882272
Pages (from-to)829-841
Number of pages13
JournalIEEE Transactions on Control of Network Systems
Volume7
Issue number2
DOIs
StatePublished - Jun 2020

Keywords

  • Accelerated method
  • distributed optimization
  • time-varying graph

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization

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