Fast Stochastic Variance Reduced Gradient Method with Momentum Acceleration for Machine Learning

TL;DR

This paper introduces FSVRG, a simplified stochastic variance reduction method with momentum acceleration that achieves optimal convergence rates and outperforms existing methods like Katyusha in various machine learning tasks.

Contribution

The paper proposes FSVRG, a novel accelerated stochastic gradient method with only one auxiliary variable and momentum, simplifying implementation and improving convergence.

Findings

FSVRG achieves linear convergence for strongly convex problems.

FSVRG attains the optimal $ ext{O}(1/T^2)$ rate for non-strongly convex problems.

Empirical results show FSVRG outperforms state-of-the-art methods like Katyusha.

Abstract

Recently, research on accelerated stochastic gradient descent methods (e.g., SVRG) has made exciting progress (e.g., linear convergence for strongly convex problems). However, the best-known methods (e.g., Katyusha) requires at least two auxiliary variables and two momentum parameters. In this paper, we propose a fast stochastic variance reduction gradient (FSVRG) method, in which we design a novel update rule with the Nesterov's momentum and incorporate the technique of growing epoch size. FSVRG has only one auxiliary variable and one momentum weight, and thus it is much simpler and has much lower per-iteration complexity. We prove that FSVRG achieves linear convergence for strongly convex problems and the optimal $\mathcal{O}(1/T^2)$ convergence rate for non-strongly convex problems, where $T$ is the number of outer-iterations. We also extend FSVRG to directly solve the problems with non-smooth component functions, such as SVM. Finally, we empirically study the performance of FSVRG for solving various machine learning problems such as logistic regression, ridge regression, Lasso and SVM. Our results show that FSVRG outperforms the state-of-the-art stochastic methods, including Katyusha.