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arXiv · 2004.07839

Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity

Haim Kaplan·Yishay Mansour·Uri Stemmer·Eliad Tsfadia
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Abstract

We present a differentially private learner for halfspaces over a finite grid $G$ in $\mathbb{R}^d$ with sample complexity $\approx d^{2.5}\cdot 2^{\log^*|G|}$, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a $d^2$ factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of $m$ linear constraints of the form $Ax\geq b$, the task is to privately identify a solution $x$ that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution $x$.

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Haim Kaplan, Yishay Mansour, Uri Stemmer, Eliad Tsfadia. 2020-04-16. Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity. https://arxiv.org/abs/2004.07839

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