Differential Privacy (DP) is a well-established framework to quantify privacy loss incurred by any algorithm. Traditional formulations impose a uniform privacy requirement for all users, which is often inconsistent with real-world scenarios in which users dictate their privacy preferences individually. This work considers the problem of mean estimation, where each user can impose their own distinct privacy level. The algorithm we propose is shown to be minimax optimal and has a near-linear run-time. Our results elicit an interesting saturation phenomenon that occurs. Namely, the privacy requirements of the most stringent users dictate the overall error rates. As a consequence, users with less but differing privacy requirements are all given more privacy than they require, in equal amounts. In other words, these privacy-indifferent users are given a nontrivial degree of privacy for free, without any sacrifice in the performance of the estimator.

翻译：差分隐私（Differential Privacy, DP）是量化算法隐私损失的标准框架。传统隐私保护方案对所有用户施加统一的隐私要求，这往往与用户自主设定隐私偏好的现实场景相悖。本研究考虑每个用户可规定不同隐私水平的均值估计问题。所提算法不仅实现了极小化最优性，还具有近线性运行时间复杂度。研究结果揭示了有趣的饱和现象：最严格用户的隐私需求决定了最终误差率。因此，隐私需求较低但存在差异的用户群体，均被赋予了超出其实际需求的同等冗余隐私保护。换言之，这些对隐私不敏感的用户无需牺牲估计器性能，即可免费获得非平凡的隐私保障水平。