arXiv subjects

Dmitriy Metelev

Publications and source records attributed to Dmitriy Metelev.

2 recordsLinked to original sources

arXiv2023

Is Consensus Acceleration Possible in Decentralized Optimization over Slowly Time-Varying Networks?

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accelerated communication rates for a certain class of time-varying graphs using a specific consensus algorithm.

math.OC↗

arXiv2022

Decentralized Saddle-Point Problems with Different Constants of Strong Convexity and Strong Concavity

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems (SPP) with strongly-convex-strongly-concave smooth objectives that have different strong convexity and strong concavity parameters of composite terms, which correspond to min and max variables, and bilinear saddle-point part. We consider two types of first-order oracles: deterministic (returns gradient) and stochastic (returns unbiased stochastic gradient). Our method works in both cases and takes several consensus steps between oracle calls.

math.OC↗