2022-06-28-block22a.md

title	abstract	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
Smoothed Online Learning is as Easy as Statistical Learning	Much of modern learning theory has been split between two regimes: the classical offline setting, where data arrive independently, and the online setting, where data arrive adversarially. While the former model is often both computationally and statistically tractable, the latter requires no distributional assumptions. In an attempt to achieve the best of both worlds, previous work proposed the smooth online setting where each sample is drawn from an adversarially chosen distribution, which is smooth, i.e., it has a bounded density with respect to a fixed dominating measure. Existing results for the smooth setting were known only for binary-valued function classes and were computation- ally expensive in general; in this paper, we fill these lacunae. In particular, we provide tight bounds on the minimax regret of learning a nonparametric function class, with nearly optimal dependence on both the horizon and smoothness parameters. Furthermore, we provide the first oracle-efficient, no-regret algorithms in this setting. In particular, we propose an oracle-efficient improper algorithm whose regret achieves optimal dependence on the horizon and a proper algorithm requiring only a single oracle call per round whose regret has the optimal horizon dependence in the classification setting and is sublinear in general. Both algorithms have exponentially worse dependence on the smoothness parameter of the adversary than the minimax rate. We then prove a lower bound on the oracle complexity of any proper learning algorithm, which matches the oracle-efficient upper bounds up to a polynomial factor, thus demonstrating the existence of a statistical-computational gap in smooth online learning. Finally, we apply our results to the contextual bandit setting to show that if a function class is learnable in the classical setting, then there is an oracle-efficient, no-regret algorithm for contextual bandits in the case that contexts arrive in a smooth manner.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	block22a	0	Smoothed Online Learning is as Easy as Statistical Learning	1716	1786	1716-1786	1716	false	Block, Adam and Dagan, Yuval and Golowich, Noah and Rakhlin, Alexander	given family Adam Block given family Yuval Dagan given family Noah Golowich given family Alexander Rakhlin	2022-06-28		Proceedings of Thirty Fifth Conference on Learning Theory	178	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v178/block22a/block22a.pdf