A key technical difficulty in differential privacy is selecting a privacy budget that satisfies privacy requirements while maximizing utility. A natural and well-studied workaround is to use personalized privacy budgets, which may differ across agents. In this paper, we show that personalized budgets come with major limitations and that for mean estimation, the dominant factor is not full personalization, but rather choosing the right effective privacy budget. This can be achieved through a simple thresholding operator that we describe. Compared with this thresholding baseline, the gains obtained by fully personalized mechanisms are limited. In particular, we precisely quantify the constant-factor improvement in settings with mixed private and public datasets and in private datasets with two levels of privacy requirements. We also establish upper bounds and identify regimes of maximal gain for arbitrary privacy requirements.

翻译：差分隐私中的一项关键技术难题是在满足隐私要求的同时选择最大化效用的隐私预算。一种常见且被广泛研究的解决思路是采用可因个体而异的个性化隐私预算。本文证明，个性化预算存在显著局限性——对于均值估计而言，决定性的因素并非完全个性化，而是选择恰当的有效隐私预算。这可以通过我们描述的简单阈值算子实现。与该阈值基线方法相比，完全个性化机制带来的增益十分有限。具体而言，我们精确量化了混合私有与公共数据集场景以及具有两层隐私要求的私有数据集场景中的常数因子改进幅度。此外，我们还建立了任意隐私要求下的上界，并确定了最大增益的适用条件。