Understanding the Role of Momentum in Stochastic Gradient Methods

TL;DR

This paper provides a unified theoretical analysis of various momentum-based stochastic gradient methods, clarifying how parameters influence convergence and offering practical guidelines for their tuning.

Contribution

It introduces a unified framework for analyzing momentum methods, revealing their convergence properties and stability, and offers new insights into parameter settings.

Findings

Unified analysis of momentum methods including heavy-ball, NAG, and QHM.

Derived conditions for convergence and stability regions.

Practical guidelines for setting learning rate and momentum parameters.

Abstract

The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks. Despite these empirical successes, there is a lack of clear understanding of how the momentum parameters affect convergence and various performance measures of different algorithms. In this paper, we use the general formulation of QHM to give a unified analysis of several popular algorithms, covering their asymptotic convergence conditions, stability regions, and properties of their stationary distributions. In addition, by combining the results on convergence rates and stationary distributions, we obtain sometimes counter-intuitive practical guidelines for setting the learning rate and momentum parameters.