2023-04-11-bajovic23a.md

title	abstract	section	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Large deviations rates for stochastic gradient descent with strongly convex functions	Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal framework for the study of general high probability bounds with SGD, based on the theory of large deviations. The framework allows for a generic (not-necessarily bounded) gradient noise satisfying mild technical assumptions, allowing for the dependence of the noise distribution on the current iterate. Under the preceding assumptions, we find an upper large deviations bound for SGD with strongly convex functions. The corresponding rate function captures analytical dependence on the noise distribution and other problem parameters. This is in contrast with conventional mean-square error analysis that captures only the noise dependence through the variance and does not capture the effect of higher order moments nor interplay between the noise geometry and the shape of the cost function. We also derive exact large deviation rates for the case when the objective function is quadratic and show that the obtained function matches the one from the general upper bound hence showing the tightness of the general upper bound. Numerical examples illustrate and corroborate theoretical findings.	Regular Papers	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bajovic23a	0	Large deviations rates for stochastic gradient descent with strongly convex functions	10095	10111	10095-10111	10095	false	Bajovic, Dragana and Jakovetic, Dusan and Kar, Soummya	given family Dragana Bajovic given family Dusan Jakovetic given family Soummya Kar	2023-04-11		Proceedings of The 26th International Conference on Artificial Intelligence and Statistics	206	inproceedings	date-parts 2023 4 11	https://proceedings.mlr.press/v206/bajovic23a/bajovic23a.pdf