A Compressed Gradient Tracking Method for Decentralized Optimization with Linear Convergence

TL;DR

This paper introduces a new compressed gradient tracking algorithm for decentralized optimization that achieves linear convergence under limited communication, unifying various compression methods.

Contribution

The paper proposes C-GT, a novel algorithm combining gradient tracking with general compression operators, achieving linear convergence for strongly convex and smooth functions.

Findings

C-GT achieves linear convergence rate.

Compatible with both unbiased and biased compressors.

Numerical results demonstrate efficiency and flexibility.

Abstract

Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multi-agent network using only local computation and peer-to-peer communication. In this paper, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm.