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arXiv 2201.03968cs.GTcs.CRcs.LG
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最优且差分隐私的数据采集:中心化与本地化机制

Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms

Fuqua School of Business(福夸商学院);Rotman School of Management(罗特曼管理学院)

Alireza Fallah, Ali Makhdoumi, Azarakhsh Malekian, Asuman Ozdaglar

AI总结:

本文研究平台从隐私敏感用户处收集数据的最优机制设计,在中心化和本地化差分隐私设置下建立极小极大下界并开发高效算法,实现最优估计与真实报告。

摘要:

我们考虑一个平台从对隐私敏感的用户处收集数据以估计感兴趣的基础参数的问题。我们将此问题表述为一个贝叶斯最优机制设计问题,其中个体可以共享其(可验证的)数据以换取金钱奖励或服务,但同时具有(私有的)异构隐私成本,我们使用差分隐私对其进行量化。我们考虑两种流行的用于为用户提供隐私保证的差分隐私设置:中心化(central)和本地化(local)。在两种设置中,我们为估计误差建立了极小极大下界,并为给定的用户异构隐私损失水平推导出(接近)最优的估计器。基于这一刻画,我们将机制设计问题表述为最优选择估计器和支付,以诱导用户真实报告其隐私敏感度。在隐私敏感度分布的规律性条件下,我们开发了高效的算法机制来解决两种隐私设置下的这一问题。我们在中心化设置中的机制可以在时间$\mathcal{O}(n \log n)$内实现,其中$n$是用户数量,而我们在本地化设置中的机制允许一个多项式时间近似方案(PTAS)。

英文摘要:

We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share her (verifiable) data in exchange for a monetary reward or services, but at the same time has a (private) heterogeneous privacy cost which we quantify using differential privacy. We consider two popular differential privacy settings for providing privacy guarantees for the users: central and local. In both settings, we establish minimax lower bounds for the estimation error and derive (near) optimal estimators for given heterogeneous privacy loss levels for users. Building on this characterization, we pose the mechanism design problem as the optimal selection of an estimator and payments that will elicit truthful reporting of users' privacy sensitivities. Under a regularity condition on the distribution of privacy sensitivities we develop efficient algorithmic mechanisms to solve this problem in both privacy settings. Our mechanism in the central setting can be implemented in time $\mathcal{O}(n \log n)$ where $n$ is the number of users and our mechanism in the local setting admits a Polynomial Time Approximation Scheme (PTAS).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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