On the sample complexity of privately learning half-spaces

Yi Hsiang Huang, Wei-Hong Chen, Shi-Chun Tsai

Keywords: Machine Learning, Differential Privacy, Computational Learning Theory, Sample Complexity, Half-spaces

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TL;DR: We prove a new sample complexity for privately learning half-space.

Abstract: We present a differentially private learner for half-spaces over a finite domain $\mathcal{X}^d\subseteq\mathbb{R}^d$ with sample complexity $\tilde{O}(d\cdot\log^*\vert\mathcal{X}\vert)$, which improves over $\tilde{O}(d^{2.5}\cdot 8^{\log^*\vert\mathcal{X}\vert})$, the state-of-the-art result of [Kaplan et al., 2020]. The building block of our result is a novel differentially private algorithm that learns half-spaces by iteratively learning thresholds on angles.

Primary Area: Trustworthy Machine Learning (accountability, explainability, transparency, causality, fairness, privacy, robustness, autoML, etc.)

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Student Author: Yes

Submission Number: 192