Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks

TL;DR

This paper introduces two communication-efficient decentralized optimization algorithms, CPP and B-CPP, that leverage gradient tracking and compression to achieve linear convergence over directed networks, reducing communication costs.

Contribution

The paper presents novel algorithms combining gradient tracking with compression for decentralized optimization over directed networks, with proven linear convergence.

Findings

CPP achieves linear convergence with unbiased compression.

B-CPP reduces communication costs further in asynchronous broadcast settings.

Numerical experiments confirm theoretical effectiveness.

Abstract

In this paper, we propose two communication efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on the objective functions. B-CPP can be applied in an asynchronous broadcast setting and further reduce communication costs compared to CPP. Numerical experiments complement the theoretical analysis and confirm the effectiveness of the proposed methods.