An Equivalence Between Private Classification and Online Prediction
Abstract: We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm. The converse direction was shown in recent work of Alon, Livni, Malliaris, and Moran, STOC '19. Together these two results show that a class of functions is privately learnable if and only if it is learnable in the mistake-bound model of online learning. To establish our result, we introduce "global stability," a new notion of algorithmic stability for learning algorithms that we show can always be satisfied when learning classes of finite Littlestone dimension.
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