On Uniform Boundedness Properties of SGD and its Momentum Variants. (arXiv:2201.10245v2 [cs.LG] UPDATED)

Web: http://arxiv.org/abs/2201.10245

A theoretical, and potentially also practical, problem with stochastic
gradient descent is that trajectories may escape to infinity. In this note, we
investigate uniform boundedness properties of iterates and function values
along the trajectories of the stochastic gradient descent algorithm and its
important momentum variant. Under smoothness and $R$-dissipativity of the loss
function, we show that broad families of step-sizes, including the widely used
step-decay and cosine with (or without) restart step-sizes, result in uniformly
bounded iterates and function values. …

arxiv lg on uniform variants