Parallel SGD: When does averaging help?

TL;DR

This paper investigates how the frequency of model averaging in parallel SGD impacts convergence, revealing that benefits depend on gradient variance and the landscape of the objective function.

Contribution

It provides a theoretical analysis of averaging frequency effects for convex and non-convex objectives, supported by multicore experiments.

Findings

Frequent averaging reduces variance in convex objectives depending on gradient variance envelope.

In non-convex objectives, averaging benefits depend on multiple global optima.

Experimental results confirm theoretical insights on synthetic and real data.

Abstract

Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and describe two ways in which the frequency of averaging affects convergence. For convex objectives, we show the benefit of frequent averaging depends on the gradient variance envelope. For non-convex objectives, we illustrate that this benefit depends on the presence of multiple globally optimal points. We complement our findings with multicore experiments on both synthetic and real data.