Private PAC learning implies finite Littlestone dimension

Abstract

We show that every approximately differentially private learning algorithm (possibly improper) for a class H with Littlestone dimension~d requires (^*(d)) examples. As a corollary it follows that the class of thresholds over N can not be learned in a private manner; this resolves open question due to [Bun et al., 2015, Feldman and Xiao, 2015]. We leave as an open question whether every class with a finite Littlestone dimension can be learned by an approximately differentially private algorithm.

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