Decentralized Saddle-Point Problems with Different Constants of Strong Convexity and Strong Concavity
Optimization and Control
2022-10-04 v2
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.
Keywords
Cite
@article{arxiv.2206.00090,
title = {Decentralized Saddle-Point Problems with Different Constants of Strong Convexity and Strong Concavity},
author = {Dmitriy Metelev and Alexander Rogozin and Alexander Gasnikov and Dmitry Kovalev},
journal= {arXiv preprint arXiv:2206.00090},
year = {2022}
}