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arXiv · 2102.07758

Decentralized Distributed Optimization for Saddle Point Problems

Alexander Rogozin·Aleksandr Beznosikov·Darina Dvinskikh·Dmitry Kovalev·Pavel Dvurechensky·Alexander Gasnikov
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Abstract

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.

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Alexander Rogozin, Aleksandr Beznosikov, Darina Dvinskikh, Dmitry Kovalev, Pavel Dvurechensky, Alexander Gasnikov. 2021-02-15. Decentralized Distributed Optimization for Saddle Point Problems. https://doi.org/10.1080/10556788.2023.2280062

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