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Poster
Understanding the Role of Momentum in Stochastic Gradient Methods
Igor Gitman · Hunter Lang · Pengchuan Zhang · Lin Xiao

Wed Dec 11 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #163

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.

Author Information

Igor Gitman (Microsoft Research)
Hunter Lang (Microsoft Research)
Pengchuan Zhang (Microsoft Research)
Lin Xiao (Microsoft Research)

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