We consider distributed convex-concave saddle point problems over arbitrary connected undirected networks and propose a decentralized distributed algorithm for their solution. The local functions distributed across the nodes are assumed to have global and local groups of variables. For the proposed algorithm we prove non-asymptotic convergence rate estimates with explicit dependence on the network characteristics. To supplement the convergence rate analysis, we propose lower bounds for strongly-convex-strongly-concave and convex-concave saddle-point problems over arbitrary connected undirected networks. We illustrate the considered problem setting by a particular application to distributed calculation of non-regularized Wasserstein barycenters.
@article{arxiv.2102.07758,
title = {Decentralized Distributed Optimization for Saddle Point Problems},
author = {Alexander Rogozin and Aleksandr Beznosikov and Darina Dvinskikh and Dmitry Kovalev and Pavel Dvurechensky and Alexander Gasnikov},
journal= {arXiv preprint arXiv:2102.07758},
year = {2024}
}