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arXiv · 2210.11869

Effects of momentum scaling for SGD

Dmitry A. Pasechnyuk·Alexander Gasnikov·Martin Takáč
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Abstract

The paper studies the properties of stochastic gradient methods with preconditioning. We focus on momentum updated preconditioners with momentum coefficient $β$. Seeking to explain practical efficiency of scaled methods, we provide convergence analysis in a norm associated with preconditioner, and demonstrate that scaling allows one to get rid of gradients Lipschitz constant in convergence rates. Along the way, we emphasize important role of $β$, undeservedly set to constant $0.99...9$ at the arbitrariness of various authors. Finally, we propose the explicit constructive formulas for adaptive $β$ and step size values.

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Dmitry A. Pasechnyuk, Alexander Gasnikov, Martin Takáč. 2022-10-21. Effects of momentum scaling for SGD. https://arxiv.org/abs/2210.11869

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