On PAC Learning Halfspaces in Non-interactive Local Privacy Model with Public Unlabeled Data

TL;DR

This paper advances PAC learning of halfspaces under non-interactive local differential privacy by leveraging public unlabeled data, achieving near-linear sample complexity under mild distribution assumptions.

Contribution

It introduces two novel approaches based on Massart noise and self-supervised learning, reducing sample complexity to linear in dimension for private and public data.

Findings

Sample complexity is linear in dimension under mild assumptions.

Proposed methods outperform previous exponential sample complexity results.

Techniques are applicable to other private PAC learning problems.

Abstract

In this paper, we study the problem of PAC learning halfspaces in the non-interactive local differential privacy model (NLDP). To breach the barrier of exponential sample complexity, previous results studied a relaxed setting where the server has access to some additional public but unlabeled data. We continue in this direction. Specifically, we consider the problem under the standard setting instead of the large margin setting studied before. Under different mild assumptions on the underlying data distribution, we propose two approaches that are based on the Massart noise model and self-supervised learning and show that it is possible to achieve sample complexities that are only linear in the dimension and polynomial in other terms for both private and public data, which significantly improve the previous results. Our methods could also be used for other private PAC learning problems.