Decentralized Gradient Tracking with Local Steps

TL;DR

This paper introduces a novel decentralized gradient tracking method, $K$-GT, that reduces communication costs through local updates while effectively handling data heterogeneity in decentralized optimization tasks.

Contribution

The paper proposes $K$-GT, a new decentralized tracking mechanism enabling communication-efficient local updates with proven convergence on non-convex functions.

Findings

Reduces communication overhead linearly with the number of local steps K

Proves convergence rate for $K$-GT on smooth non-convex functions

Demonstrates robustness on convex and non-convex benchmarks and neural network training

Abstract

Gradient tracking (GT) is an algorithm designed for solving decentralized optimization problems over a network (such as training a machine learning model). A key feature of GT is a tracking mechanism that allows to overcome data heterogeneity between nodes. We develop a novel decentralized tracking mechanism, $K$-GT, that enables communication-efficient local updates in GT while inheriting the data-independence property of GT. We prove a convergence rate for $K$-GT on smooth non-convex functions and prove that it reduces the communication overhead asymptotically by a linear factor $K$, where $K$ denotes the number of local steps. We illustrate the robustness and effectiveness of this heterogeneity correction on convex and non-convex benchmark problems and on a non-convex neural network training task with the MNIST dataset.