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Effects of momentum scaling for SGD
Dmitry A. Pasechnyuk · Alexander Gasnikov · Martin Takac
The paper studies the properties of stochastic gradient methods with preconditioning. We focus on momentum updated preconditioners with momentum coefficient $\beta$. 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 $\beta$, undeservedly set to constant $0.99...9$ at the arbitrariness of various authors. Finally, we propose the explicit constructive formulas for adaptive $\beta$ and step size values.

Author Information

Dmitry A. Pasechnyuk (Mohamed bin Zayed University of Artificial Intelligence)
Alexander Gasnikov (Moscow Institute of Physics and Technology)
Martin Takac (Mohamed bin Zayed University of Artificial Intelligence (MBZUAI))

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