  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.
