Min-max optimization over slowly time-varying graphs

TL;DR

This paper investigates decentralized min-max optimization over slowly changing networks, demonstrating that limited edge modifications per iteration suffice for convergence and identifying classes of graphs with reduced communication complexity.

Contribution

It introduces a framework for min-max optimization on slowly time-varying graphs and shows that minimal edge changes per iteration maintain convergence, with reduced complexity for specific graph classes.

Findings

Changing only two edges per iteration suffices for convergence.

Certain classes of time-varying graphs allow reduced communication complexity.

The approach extends decentralized optimization to saddle point problems on dynamic networks.

Abstract

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max optimization for saddle point problems. Saddle point problems arise in training adversarial networks and in robust machine learning. The focus of the work is optimization over (slowly) time-varying networks. The topology of the network changes from time to time, and the velocity of changes is limited. We show that, analogically to decentralized optimization, it is sufficient to change only two edges per iteration in order to slow down convergence to the arbitrary time-varying case. At the same time, we investigate several classes of time-varying graphs for which the communication complexity can be reduced.