Distributed Optimization over Time-varying Graphs with Imperfect Sharing of Information
Abstract
We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this paper, we propose and study a two time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. For strongly convex loss functions, with a proper choice of step-sizes, we show that the agents' estimates converge to the global optimal state at a rate of . Another important contribution of this work is to provide novel tools to deal with diminishing average weights over time-varying graphs.
Cite
@article{arxiv.2106.08469,
title = {Distributed Optimization over Time-varying Graphs with Imperfect Sharing of Information},
author = {Hadi Reisizadeh and Behrouz Touri and Soheil Mohajer},
journal= {arXiv preprint arXiv:2106.08469},
year = {2022}
}