Understanding the Impact of Model Incoherence on Convergence of Incremental SGD with Random Reshuffle

TL;DR

This paper investigates how model incoherence influences the convergence behavior of SGD with random reshuffle, revealing that certain incoherence measures can improve convergence speed and accuracy.

Contribution

It introduces the concept of model incoherence to analyze its effect on SGD convergence, providing theoretical insights into the benefits of random reshuffle.

Findings

Model incoherence affects convergence error and rate.

SGD with random reshuffle converges faster under certain incoherence conditions.

Results justify the practical superiority of random reshuffle in SGD.

Abstract

Although SGD with random reshuffle has been widely-used in machine learning applications, there is a limited understanding of how model characteristics affect the convergence of the algorithm. In this work, we introduce model incoherence to characterize the diversity of model characteristics and study its impact on convergence of SGD with random reshuffle under weak strong convexity. Specifically, minimizer incoherence measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle. In particular, we show that the variable sequence generated by SGD with random reshuffle converges to a certain global minimizer of the total loss under full minimizer coherence. The other curvature incoherence measures the quality of condition numbers of the sample losses and determines the convergence rate of SGD. With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to the superior practical performance of SGD with random reshuffle.