Error Compensated Loopless SVRG, Quartz, and SDCA for Distributed Optimization

TL;DR

This paper introduces three new error compensated gradient methods—EC-LSVRG, EC-Quartz, and EC-SDCA—for distributed optimization, achieving improved convergence rates and reduced communication costs through error compensation and gradient compression techniques.

Contribution

The paper proposes and analyzes three novel error compensated methods compatible with contraction compressors, providing theoretical convergence guarantees and demonstrating efficiency through experiments.

Findings

Linear convergence rates for EC-LSVRG in convex and smooth cases.

EC-Quartz and EC-SDCA achieve convergence rates comparable to EC-LSVRG.

Numerical experiments confirm the efficiency of the proposed methods.

Abstract

The communication of gradients is a key bottleneck in distributed training of large scale machine learning models. In order to reduce the communication cost, gradient compression (e.g., sparsification and quantization) and error compensation techniques are often used. In this paper, we propose and study three new efficient methods in this space: error compensated loopless SVRG method (EC-LSVRG), error compensated Quartz (EC-Quartz), and error compensated SDCA (EC-SDCA). Our method is capable of working with any contraction compressor (e.g., TopK compressor), and we perform analysis for convex optimization problems in the composite case and smooth case for EC-LSVRG. We prove linear convergence rates for both cases and show that in the smooth case the rate has a better dependence on the parameter associated with the contraction compressor. Further, we show that in the smooth case, and under some certain conditions, error compensated loopless SVRG has the same convergence rate as the vanilla loopless SVRG method. Then we show that the convergence rates of EC-Quartz and EC-SDCA in the composite case are as good as EC-LSVRG in the smooth case. Finally, numerical experiments are presented to illustrate the efficiency of our methods.