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：我们考虑了分流的连接点问题,涉及任意连接的无方向网络,并提出一个分散的分布式算法来解决这些网络。各节点分布的地方功能假定有全球和地方的变数组。关于拟议的算法,我们证明,非同步汇合率估计数明显依赖网络特性。为了补充汇合率分析,我们建议,对于任意连接的无方向网络,为强凝聚和凝聚点问题设定较低的界限。我们通过特别应用来分配非常规的瓦塞斯坦百货中心。我们用一个特定应用来说明所考虑的问题设置。