一句话：证明在连续查询的差分隐私中，Laplace 机制在给定隐私约束下达到最优效用，推广了离散情形的几何机制最优性。
差分隐私通过在统计查询结果上施加混淆机制保护个体数据，但会降低效用。已有工作证明：对离散数据（如计数查询），在给定隐私程度和合理效用损失下，几何机制最优，效用损失最小；但该结论对连续查询结果（如实数）不成立。本文利用此前的离散结果、抽象信道及其超分布几何表示，以及 Kantorovich-Rubinstein 定理提供的分布距离对偶解释，证明在连续查询场景下，采用 Laplace 机制进行混淆可重新获得最优性。即 Laplace 机制在满足隐私约束的同时实现尽可能小的效用损失，从而把离散情形的最优性推广到连续查询。
Differential Privacy protects individuals’ data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also decreases its utility. Yet it has been shown that for discrete data (e.g. counting queries), a mandated degree of privacy and a reasonable interpretation of loss of utility, the Geometric obfuscating mechanism is optimal: it loses as little utility as possible [Ghosh et al. [1]].For continuous query results however (e.g. real numbers) the optimality result does not hold. Our contribution here is to show that optimality is regained by using the Laplace mechanism for the obfuscation.The technical apparatus involved includes the earlier discrete result [Ghosh op. cit.], recent work on abstract channels and their geometric representation as hyper-distributions [Alvim et al. [2]], and the dual interpretations of distance between distributions provided by the Kantorovich-Rubinstein Theorem.
@inproceedings{paperbot6204,
title = {The Laplace Mechanism has optimal utility for differential privacy over continuous queries},
author = {Natasha Fernandes and Annabelle McIver and Carroll Morgan},
booktitle = {LICS},
year = {2021},
doi = {10.1109/lics52264.2021.9470718}
}