@inproceedings{2b80ee6c630343f1840166880bd0180d,
title = "Adversarial laws of large numbers and optimal regret in online classification",
abstract = "Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can affect the environment they are acting upon and interact with it. Specifically, we consider the sequential sampling model proposed by Ben-Eliezer and Yogev (2020), and characterize the classes which admit a uniform law of large numbers in this model: these are exactly the classes that are online learnable. Our characterization may be interpreted as an online analogue to the equivalence between learnability and uniform convergence in statistical (PAC) learning. The sample-complexity bounds we obtain are tight for many parameter regimes, and as an application, we determine the optimal regret bounds in online learning, stated in terms of Littlestone's dimension, thus resolving the main open question from Ben-David, P{\'a}l, and Shalev-Shwartz (2009), which was also posed by Rakhlin, Sridharan, and Tewari (2015).",
keywords = "Littlestone dimension, adversarial robustness, online learning, random sampling, robust sampling",
author = "Noga Alon and Omri Ben-Eliezer and Yuval Dagan and Shay Moran and Moni Naor and Eylon Yogev",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",
year = "2021",
month = jun,
day = "15",
doi = "10.1145/3406325.3451041",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Association for Computing Machinery",
pages = "447--455",
editor = "Samir Khuller and Williams, \{Virginia Vassilevska\}",
booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",
address = "الولايات المتّحدة",
}