Private Learning of Halfspaces: Simplifying the Construction and Reducing the Sample Complexity
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We present a differentially private learner for halfspaces over a finite grid G in R^d with sample complexity ≈ d^2.5· 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≥ 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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