Understanding the Role of Momentum in Stochastic Gradient Methods
This work addresses a fundamental issue for machine learning practitioners using momentum-based optimization, offering incremental theoretical insights.
The paper tackles the lack of clear understanding of how momentum parameters affect convergence and performance in stochastic gradient methods, providing a unified analysis of popular algorithms and deriving practical guidelines for parameter settings.
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.