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.

翻译：本文考虑任意连通无向网络上的分布式凸凹鞍点问题，并提出一种去中心化分布式算法以求解该问题。假设分布在网络各节点上的局部函数具有全局变量组和局部变量组。针对所提算法，我们证明了具有网络特性显式依赖的非渐近收敛率估计。为补充收敛率分析，我们给出了任意连通无向网络上强凸-强凹与凸-凹鞍点问题的下界。通过非正则化Wasserstein重心分布式计算这一具体应用实例，我们阐释了所考虑的问题设定。