[论文解读] Selling Privacy at Auction

Arpita Ghosh, Aaron Roth|ScholarlyCommons (University of Pennsylvania)|Nov 5, 2010

Privacy-Preserving Technologies in Data参考文献 16被引用 5

一句话总结

本文提出了一种新颖的拍卖框架，用于在确保差分隐私的前提下购买私人数据，将数据分析师的采购行为建模为多单位采购拍卖。研究表明，可以设计出最优机制，在满足精度目标时最小化成本，或在预算约束下最大化精度，但个体理性与强隐私保证无法共存而不引入偏差。

ABSTRACT

We initiate the study of markets for private data, though the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply. On the other hand, the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such auctions can naturally be viewed and optimally solved as variants of multi-unit procurement auctions. Based on this result, we derive auctions for two natural settings which are optimal up to small constant factors: 1. In the setting in which the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst's accuracy goal while minimizing his total payment. 2. In the setting in which the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analysts budget. In both cases, our comparison class is the set of envy-free mechanisms, which correspond to the natural class of fixed-price mechanisms in our setting. In both of these results, we ignore the privacy cost due to possible correlations between an individuals private data and his valuation for privacy itself. We then show that generically, no individually rational mechanism can compensate individuals for the privacy loss incurred due to their reported valuations for privacy.

研究动机与目标

• 将私人数据市场形式化为一个机制设计问题，其中差分隐私作为可量化的商品。
• 解决公平补偿数据所有者隐私损失的问题，同时确保总体估计的准确性。
• 在两个关键约束下识别最优拍卖机制：固定的精度目标和严格的预算限制。
• 探索在强隐私模型下，个体理性机制的理论极限。

提出的方法

• 将数据分析师的问题建模为多单位采购拍卖，其中投标人（数据所有者）报告隐私成本。
• 使用差分隐私作为正式保证来量化隐私损失，并支持对隐私成本的效用理论解释。
• 通过与无嫉妒定价基准进行比较，推导出最优拍卖机制，实现在常数因子内的近似最优性。
• 应用差分隐私的组合性质，以界定跨所有投标人的总隐私损失。
• 提出一个形式化的不可能性结果，表明在严格隐私模型下，任何个体理性机制都无法实现非平凡精度，其中数据和估值隐私均受到保护。
• 提出未来研究方向，包括有界估值、说谎激励以及动态或多市场环境下的机制设计。

实验结果

研究问题

• RQ1 能否在市场环境中高效且公平地使用差分隐私作为可量化的度量来购买私人数据？
• RQ2 数据分析师应如何设计拍卖机制，以在实现固定精度目标的前提下最小化支付？
• RQ3 当数据分析师面临严格预算限制时，哪种拍卖机制能最大化精度？
• RQ4 是否可以设计一种机制，公平补偿个体因自身数据与报告隐私估值之间相关性而导致的隐私损失？
• RQ5 当数据和估值隐私均受到保护时，个体理性机制的根本局限是什么？

主要发现

• 对于具有固定精度目标的数据分析师，可以设计出最优拍卖机制，在常数因子内实现成本最小化，接近最优无嫉妒定价。
• 对于具有严格预算限制的数据分析师，所提出的机制在常数因子内实现了最优无嫉妒机制的精度最大化。
• 证明了一个根本性的不可能性结果：在严格隐私模型下，任何个体理性机制都无法实现非平凡精度，其中数据和估值隐私均受到保护。
• 由于精度和差分隐私约束，所有投标人的总隐私损失必须至少为 ln(4/3) ≈ 0.2875，无论个体估值如何。
• 有界的估值范围可以规避不可能性结果，但会重新引入抽样偏差，从而损害代表性估计的目标。
• 本文识别出五个关键未来研究方向，包括动态拍卖、多市场机制，以及处理数据报告中的说谎激励问题。