Variance Reduced Stochastic Gradient Descent with Neighbors

TL;DR

This paper introduces a novel variance reduction algorithm for stochastic gradient descent that leverages neighborhood structures in data to improve convergence speed during early training phases.

Contribution

It proposes a new class of memorization algorithms that share gradient information among neighboring data points, with a unified convergence analysis.

Findings

Experimental results support the theoretical convergence claims.

The method accelerates early-stage training compared to traditional variance reduction techniques.

Unified analysis applies to a broad family of variance reduction algorithms.

Abstract

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence. However, these methods are either based on computations of full gradients at pivot points, or on keeping per data point corrections in memory. Therefore speed-ups relative to SGD may need a minimal number of epochs in order to materialize. This paper investigates algorithms that can exploit neighborhood structure in the training data to share and re-use information about past stochastic gradients across data points, which offers advantages in the transient optimization phase. As a side-product we provide a unified convergence analysis for a family of variance reduction algorithms, which we call memorization algorithms. We provide experimental results supporting our theory.