posted on 2024-10-25, 10:12authored byAnton RodomanovAnton Rodomanov, Ali Kavis, Yongtao Wu, Kimon Antonakopoulos, Volkan Cevher
We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle’s noise but also to the Hölder smoothness of the objective function without a priori knowledge of the particular setting. The key ingredient is a novel strategy for adjusting step-size coefficients in the Stochastic Gradient Method (SGD). Unlike AdaGrad, which accumulates gradient norms, our Universal Gradient Method accumulates appropriate combinations of gradientand iterate differences. The resulting algorithm has state-of-the-art worst-case convergence rate guarantees for the entire Hölder class including, in particular, both nonsmooth functions and those with Lipschitz continuous gradient. We also present the Universal Fast Gradient Method for SCO enjoying optimal efficiency estimates.
History
Primary Research Area
Trustworthy Information Processing
Name of Conference
International Conference on Machine Learning (ICML)
Journal
Proceedings of the 41st International Conference on Machine Learning
Volume
235
Page Range
42620-42646
Publisher
PMLR
BibTeX
@conference{Rodomanov:Kavis:Wu:Antonakopoulos:Cevher:2024,
title = "Universal Gradient Methods for Stochastic Convex Optimization",
author = "Rodomanov, Anton" AND "Kavis, Ali" AND "Wu, Yongtao" AND "Antonakopoulos, Kimon" AND "Cevher, Volkan",
year = 2024,
month = 7,
journal = "Proceedings of the 41st International Conference on Machine Learning",
pages = "42620--42646",
publisher = "PMLR"
}