Private PAC learning implies finite Littlestone dimension

4 Jun 2018  ·  Noga Alon, Roi Livni, Maryanthe Malliaris, Shay Moran ·

We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\Omega\bigl(\log^*(d)\bigr)$ examples. As a corollary it follows that the class of thresholds over $\mathbb{N}$ 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. read more

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