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Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
Haim Kaplan · Yishay Mansour · Uri Stemmer · Eliad Tsfadia

Tue Dec 08 09:00 AM -- 11:00 AM (PST) @ Poster Session 1 #256
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 {\em privately} identify a solution $x$ that satisfies {\em most} of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution $x$.

Author Information

Haim Kaplan (TAU, GOOGLE)
Yishay Mansour (Tel Aviv University / Google)
Uri Stemmer (Ben-Gurion University and Google Research)
Eliad Tsfadia (Tel Aviv University and Google)

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