Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
(2004.07839)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 $d2$ 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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