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

• URL: http://arxiv.org/abs/2004.07839v2
• Date: Tue, 3 Nov 2020 09:44:34 GMT
• Title: Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
• Authors: Haim Kaplan, Yishay Mansour, Uri Stemmer, Eliad Tsfadia
• Abstract summary: We present a differentially private learner for halfspaces over a finite grid $G$ in $mathbbRd$ with sample complexity $approx d2.5cdot 2log*|G|$. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem.
• Score: 63.29100726064574
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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