A simpler approach to accelerated optimization: iterative averaging meets optimism
Pooria Joulani, Anant Raj, Andras Gyorgy, Csaba Szepesvari
Abstract
Recently there have been several attempts to extend Nesterov’s accelerated algorithm to smooth stochastic and variance-reduced optimization. In this paper, we show that there is a simpler approach to acceleration: applying optimistic online learning algorithms and querying the gradient oracle at the online average of the intermediate optimization iterates. In particular, we tighten a recent result of Cutkosky (2019) to demonstrate theoretically that online iterate averaging results in a reduced optimization gap, independently of the algorithm involved. We show that carefully combining this technique with existing generic optimistic online learning algorithms yields the optimal accelerated rates for optimizing strongly-convex and non-strongly-convex, possibly composite objectives, with deterministic as well as stochastic first-order oracles. We further extend this idea to variance-reduced optimization. Finally, we also provide “universal” algorithms that achieve the optimal rate for smooth and non-smooth composite objectives simultaneously without further tuning, generalizing the results of Kavis et al. (2019) and solving a number of their open problems.
BibTeX
@InProceedings{pmlr-v119-joulani20a,
title = {A simpler approach to accelerated optimization: iterative averaging meets optimism},
author = {Joulani, Pooria and Raj, Anant and Gyorgy, Andras and Szepesvari, Csaba},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {4984--4993},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/joulani20a/joulani20a.pdf},
url = {https://proceedings.mlr.press/v119/joulani20a.html},
abstract = {Recently there have been several attempts to extend Nesterov’s accelerated algorithm to smooth stochastic and variance-reduced optimization. In this paper, we show that there is a simpler approach to acceleration: applying optimistic online learning algorithms and querying the gradient oracle at the online average of the intermediate optimization iterates. In particular, we tighten a recent result of Cutkosky (2019) to demonstrate theoretically that online iterate averaging results in a reduced optimization gap, independently of the algorithm involved. We show that carefully combining this technique with existing generic optimistic online learning algorithms yields the optimal accelerated rates for optimizing strongly-convex and non-strongly-convex, possibly composite objectives, with deterministic as well as stochastic first-order oracles. We further extend this idea to variance-reduced optimization. Finally, we also provide “universal” algorithms that achieve the optimal rate for smooth and non-smooth composite objectives simultaneously without further tuning, generalizing the results of Kavis et al. (2019) and solving a number of their open problems.}
}