Decentralized optimization over slowly time-varying graphs: algorithms and lower bounds

Dmitry Metelev (), Aleksandr Beznosikov (), Alexander Rogozin (), Alexander Gasnikov () and Anton Proskurnikov
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Dmitry Metelev: Moscow Institute of Physics and Technology
Aleksandr Beznosikov: Moscow Institute of Physics and Technology
Alexander Rogozin: Moscow Institute of Physics and Technology
Alexander Gasnikov: Moscow Institute of Physics and Technology

Computational Management Science, 2024, vol. 21, issue 1, No 8, 25 pages

Abstract: Abstract We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or time-varying network. Our main concern is the convergence rate of first-order optimization algorithms as a function of the network’s graph, more specifically, of the condition numbers of gossip matrices. We are interested in the case when the network is time-varying but the rate of changes is restricted. We study two cases: randomly changing network satisfying Markov property and a network changing in a deterministic manner. For the random case, we propose a decentralized optimization algorithm with accelerated consensus. For the deterministic scenario, we show that if the graph is changing in a worst-case way, accelerated consensus is not possible even if only two edges are changed at each iteration. The fact that such a low rate of network changes is sufficient to make accelerated consensus impossible is novel and improves the previous results in the literature.

Keywords: Convex optimization; Decentralized optimization; Time-varying network; Consensus; Convergence rate (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-023-00489-5

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