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arXiv · 2206.00090

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

Dmitriy Metelev·Alexander Rogozin·Alexander Gasnikov·Dmitry Kovalev
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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 (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.

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Dmitriy Metelev, Alexander Rogozin, Alexander Gasnikov, Dmitry Kovalev. 2022-05-31. Decentralized Saddle-Point Problems with Different Constants of Strong Convexity and Strong Concavity. https://arxiv.org/abs/2206.00090

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