When and Why Momentum Accelerates SGD:An Empirical Study
This work provides empirical insights into optimizer behavior for deep learning practitioners, though it is incremental in refining existing momentum understanding.
The study investigates when and why momentum accelerates stochastic gradient descent (SGD), finding that SGD with momentum (SGDM) outperforms SGD when effective learning rates exceed a threshold, with advantages increasing with larger batch sizes, and links this acceleration to preventing abrupt sharpening in the loss landscape.
Momentum has become a crucial component in deep learning optimizers, necessitating a comprehensive understanding of when and why it accelerates stochastic gradient descent (SGD). To address the question of ''when'', we establish a meaningful comparison framework that examines the performance of SGD with Momentum (SGDM) under the \emph{effective learning rates} $η_{ef}$, a notion unifying the influence of momentum coefficient $μ$ and batch size $b$ over learning rate $η$. In the comparison of SGDM and SGD with the same effective learning rate and the same batch size, we observe a consistent pattern: when $η_{ef}$ is small, SGDM and SGD experience almost the same empirical training losses; when $η_{ef}$ surpasses a certain threshold, SGDM begins to perform better than SGD. Furthermore, we observe that the advantage of SGDM over SGD becomes more pronounced with a larger batch size. For the question of ``why'', we find that the momentum acceleration is closely related to \emph{abrupt sharpening} which is to describe a sudden jump of the directional Hessian along the update direction. Specifically, the misalignment between SGD and SGDM happens at the same moment that SGD experiences abrupt sharpening and converges slower. Momentum improves the performance of SGDM by preventing or deferring the occurrence of abrupt sharpening. Together, this study unveils the interplay between momentum, learning rates, and batch sizes, thus improving our understanding of momentum acceleration.