Littlestone Classes are Privately Online Learnable

Noah Golowich, Roi Livni

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

We consider the problem of online classification under a privacy constraint. In this setting a learner observes sequentially a stream of labelled examples (xt, yt), for 1 ≤ t ≤ T, and returns at each iteration t a hypothesis ℎt which is used to predict the label of each new example xt. The learner's performance is measured by her regret against a known hypothesis class H. We require that the algorithm satisfies the following privacy constraint: the sequence ℎ1,..., ℎT of hypotheses output by the algorithm needs to be an (ǫ, δ)-differentially private function of the whole input sequence (x1, y1),..., (xT, yT ). We provide the first non-trivial regret bound for the realizable setting. Specifically, we show that if the class H has constant Littlestone dimension then, given an oblivious sequence of labelled examples, there is a private learner that makes in expectation at most O(logT) mistakes - comparable to the optimal mistake bound in the non-private case, up to a logarithmic factor. Moreover, for general values of the Littlestone dimension d, the same mistake bound holds but with a doubly-exponential in d factor. A recent line of work has demonstrated a strong connection between classes that are online learnable and those that are differentially-private learnable. Our results strengthen this connection and show that an online learning algorithm can in fact be directly privatized (in the realizable setting). We also discuss an adaptive setting and provide a sublinear regret bound of O(T).

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
EditorsMarc'Aurelio Ranzato, Alina Beygelzimer, Yann Dauphin, Percy S. Liang, Jenn Wortman Vaughan
PublisherNeural information processing systems foundation
Pages11462-11473
Number of pages12
ISBN (Electronic)9781713845393
StatePublished - 2021
Event35th Conference on Neural Information Processing Systems, NeurIPS 2021 - Virtual, Online
Duration: 6 Dec 202114 Dec 2021

Publication series

NameAdvances in Neural Information Processing Systems
Volume14
ISSN (Print)1049-5258

Conference

Conference35th Conference on Neural Information Processing Systems, NeurIPS 2021
CityVirtual, Online
Period6/12/2114/12/21

Funding

FundersFunder number
National Science Foundation
Hertz Foundation
Google
Iowa Science Foundation2188/20
Tel Aviv University

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