@inproceedings{89f75603ef9d4601b8a8ba104d689383,

title = "Privately Learning Thresholds: Closing the Exponential Gap",

abstract = "We present a private agnostic learner for halfspaces over an arbitrary finite domain X ⊂ R d with sample complexity poly(d, 2log∗|X|). The building block for this learner is a differentially private algorithm for locating an approximate center point of m > poly(d, 2log∗|X|) points – a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al. FOCS {\textquoteright}15]. This relationship suggests that the problem of privately locating a center point may have further applications in the design of differentially private algorithms. We also provide a lower bound on the sample complexity for privately finding a point in the convex hull. For approximate differential privacy, we show a lower bound of m = Ω(d+log∗|X|), whereas for pure differential privacy m = Ω(d log |X|). Keywords: Differential privacy, Private PAC learning, Halfspaces, Quasi-concave functions",

author = "Haim Kaplan and Katrina Ligett and Yishay Mansour and Moni Naor and Uri Stemmer",

year = "2020",

language = "אנגלית",

volume = "125",

series = "Proceedings of Machine Learning Research",

publisher = "PMLR",

pages = "2263--2285",

editor = "Abernethy, {Jacob D.} and Shivani Agarwal",

booktitle = "Conference on Learning Theory, COLT 2020, 9-12 July 2020, Virtual Event [Graz, Austria]",

}