Decentralized saddle-point problems with different constants of strong convexity and strong concavity

Dmitry Metelev (), Alexander Rogozin (), Alexander Gasnikov () and Dmitry Kovalev ()
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Dmitry Metelev: Moscow Institute of Physics and Technology
Alexander Rogozin: Moscow Institute of Physics and Technology
Alexander Gasnikov: Moscow Institute of Physics and Technology
Dmitry Kovalev: King Abdullah University of Science and Technology

Computational Management Science, 2024, vol. 21, issue 1, No 5, 41 pages

Abstract: Abstract 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 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.

Keywords: Decentralized optimization; Time-varying graphs; Saddle-point problem; Stochastic optimization; Consensus subroutine; Inexact oracle (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10287-023-00485-9

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