Asymptotic Network Independence in Distributed Stochastic Optimization for Machine Learning

TL;DR

This paper discusses the asymptotic network independence property in distributed stochastic optimization, showing how distributed methods can asymptotically match centralized solutions in machine learning tasks.

Contribution

It introduces the concept of asymptotic network independence and provides a mathematical analysis comparing distributed stochastic gradient descent with centralized SGD.

Findings

Distributed methods can asymptotically match centralized convergence rates.

The analysis demonstrates conditions under which network effects diminish.

The property holds in certain scenarios, overcoming network-induced barriers.

Abstract

We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property, which is achieved whenever a distributed method executed over a network of n nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network. We explain this property through an example involving the training of ML models and sketch a short mathematical analysis for comparing the performance of distributed stochastic gradient descent (DSGD) with centralized stochastic gradient decent (SGD).