Decentralized convex optimization on time-varying networks with application to Wasserstein barycenters

Olga Yufereva (), Michael Persiianov (), Pavel Dvurechensky (), Alexander Gasnikov () and Dmitry Kovalev ()
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Olga Yufereva: N. N. Krasovskii Institute of Mathematics and Mechanics
Michael Persiianov: Moscow Institute of Physics and Technology
Pavel Dvurechensky: Weierstrass Institute for Applied Analysis and Stochastics
Alexander Gasnikov: Moscow Institute of Physics and Technology
Dmitry Kovalev: Université catholique de Louvain (UCL)

Computational Management Science, 2024, vol. 21, issue 1, No 12, 31 pages

Abstract: Abstract Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are motivated by examples when only a subset of sensors can observe each time step, and yet, the goal is to average signals (e.g., satellite pictures of some area) by approximating their barycenter. We embed this problem into a class of non-smooth dual-friendly distributed optimization problems over time-varying networks and develop a first-order method for this class. We prove non-asymptotic accelerated in the sense of Nesterov convergence rates and explicitly characterize their dependence on the parameters of the network and its dynamics. In the experiments, we demonstrate the efficiency of the proposed algorithm when applied to the Wasserstein barycenter problem.

Keywords: Distributed optimization; Dual oracle; Wasserstein barycenter; Time-varying networks; Consensus problem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-023-00493-9

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