Asynchronous stochastic convex optimization

TL;DR

This paper demonstrates that asynchronous stochastic gradient methods can achieve near-optimal convergence rates for convex optimization, with empirical evidence showing their robustness and efficiency in parallel settings.

Contribution

It proves asymptotic optimality of asynchronous stochastic gradient procedures under conditions similar to standard methods and provides empirical validation of their strong performance.

Findings

Asynchronous methods attain optimal convergence rates.

Robustness of stochastic approximation enables faster parallel solutions.

Empirical results confirm efficiency of asynchronous schemes.

Abstract

We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for asymptotic optimality of standard stochastic gradient procedures. Roughly, the noise inherent to the stochastic approximation scheme dominates any noise from asynchrony. We also give empirical evidence demonstrating the strong performance of asynchronous, parallel stochastic optimization schemes, demonstrating that the robustness inherent to stochastic approximation problems allows substantially faster parallel and asynchronous solution methods.