Near-Optimal Decentralized Algorithms for Saddle Point Problems over Time-Varying Networks

TL;DR

This paper develops near-optimal decentralized algorithms for saddle point problems over dynamic networks, addressing real-world issues like network changes and establishing theoretical complexity bounds.

Contribution

It introduces algorithms that achieve near-optimal performance for saddle point problems in time-varying network settings, matching established lower bounds.

Findings

Established lower complexity bounds for the problem setup.

Developed algorithms that meet these lower bounds.

Addressed network malfunctions by allowing topology changes.

Abstract

Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type, where the summands are held by separate computational entities connected by a network. The network topology may change from time to time, which models real-world network malfunctions. We obtain lower complexity bounds for algorithms in this setup and develop near-optimal methods which meet the lower bounds.