Efficient Private Algorithms for Learning Large-Margin Halfspaces

TL;DR

This paper introduces differentially private algorithms for large-margin halfspace learning whose sample complexity depends solely on the margin, not the data dimension, and proves this dependence is optimal.

Contribution

The paper proposes novel privacy-preserving algorithms with margin-dependent sample complexity and establishes their optimality through lower bounds.

Findings

Sample complexity depends only on margin, not dimension

Algorithms are differentially private for large-margin halfspaces

Lower bounds confirm the optimality of the margin dependence

Abstract

We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex optimization, the sample complexity of our algorithms depends only on the margin of the data, and not on the dimension. We complement our results with a lower bound, showing that the dependence of our upper bounds on the margin is optimal.