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

Jinyan Su, Jinhui Xu, Di Wang
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引用次数: 2

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.
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具有公共未标记数据的非交互式局部隐私模型的PAC学习半空间
本文研究了非交互局部差分隐私模型(NLDP)中的PAC学习半空间问题。为了突破指数样本复杂性的障碍,之前的结果研究了一个宽松的设置,其中服务器可以访问一些额外的公共但未标记的数据。我们继续朝这个方向前进。具体来说,我们考虑的是标准设定下的问题,而不是之前研究的大保证金设定。在对底层数据分布的不同温和假设下,我们提出了两种基于Massart噪声模型和自监督学习的方法,并表明对于私有和公共数据都有可能实现仅在维度上是线性的、在其他方面是多项式的样本复杂性,这大大改进了之前的结果。我们的方法也可以用于其他私人PAC学习问题。
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