Towards Optimal One Pass Large Scale Learning with Averaged Stochastic Gradient Descent

TL;DR

This paper analyzes averaged stochastic gradient descent (ASGD) for large-scale learning, showing that proper learning rate setting significantly improves its efficiency and effectiveness in reaching optimal models in fewer samples.

Contribution

It provides a finite sample analysis of ASGD, proposes a simple method to set the learning rate properly, and demonstrates its superiority over other algorithms in large-scale linear classification.

Findings

Proper learning rate setting reduces samples needed for ASGD to reach asymptotic performance.

ASGD with the proposed learning rate outperforms other algorithms in experiments.

Finite sample analysis explains the practical efficiency of ASGD in large-scale learning.

Abstract

For large scale learning problems, it is desirable if we can obtain the optimal model parameters by going through the data in only one pass. Polyak and Juditsky (1992) showed that asymptotically the test performance of the simple average of the parameters obtained by stochastic gradient descent (SGD) is as good as that of the parameters which minimize the empirical cost. However, to our knowledge, despite its optimal asymptotic convergence rate, averaged SGD (ASGD) received little attention in recent research on large scale learning. One possible reason is that it may take a prohibitively large number of training samples for ASGD to reach its asymptotic region for most real problems. In this paper, we present a finite sample analysis for the method of Polyak and Juditsky (1992). Our analysis shows that it indeed usually takes a huge number of samples for ASGD to reach its asymptotic region for improperly chosen learning rate. More importantly, based on our analysis, we propose a simple way to properly set learning rate so that it takes a reasonable amount of data for ASGD to reach its asymptotic region. We compare ASGD using our proposed learning rate with other well known algorithms for training large scale linear classifiers. The experiments clearly show the superiority of ASGD.