Perturbed Iterate Analysis for Asynchronous Stochastic Optimization

TL;DR

This paper introduces a unified perturbed iterate framework for analyzing asynchronous stochastic optimization algorithms, simplifying existing analyses and enabling the development of faster parallel algorithms like KroMagnon.

Contribution

The paper presents a novel perturbed iterate analysis framework that simplifies and improves the understanding of asynchronous stochastic optimization methods, and introduces KroMagnon, a faster parallel SVRG algorithm.

Findings

Simplified analysis of Hogwild! and asynchronous coordinate descent.

Improved convergence bounds for asynchronous algorithms.

KroMagnon achieves over four orders of magnitude speedup in experiments.

Abstract

We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optimization algorithms can be thought of as serial methods operating on noisy inputs. Using our perturbed iterate framework, we provide new analyses of the Hogwild! algorithm and asynchronous stochastic coordinate descent, that are simpler than earlier analyses, remove many assumptions of previous models, and in some cases yield improved upper bounds on the convergence rates. We proceed to apply our framework to develop and analyze KroMagnon: a novel, parallel, sparse stochastic variance-reduced gradient (SVRG) algorithm. We demonstrate experimentally on a 16-core machine that the sparse and parallel version of SVRG is in some cases more than four orders of magnitude faster than the standard SVRG algorithm.