使用隐私感知代理的最佳数据采集
Optimal Data Acquisition with Privacy-Aware Agents
摘要：
我们研究了希望从隐私感知代理收集私人数据的数据分析师或平台所面临的问题。为了激励参与，作为对这些数据的交换，平台以使用所有代理提交的数据计算的统计数据的形式向代理提供服务。代理商通过考虑加入平台的隐私成本和他们从获得统计数据中获得的利益来决定是否加入平台（并如实披露他们的数据）或不参与。平台必须确保统计数据是以差异化的方式私下计算的，并选择一个中心噪声水平添加到计算中，但也可以通过根据不同代理的异构隐私偏好（平台已知）在计算中为不同代理提供不同权重来诱导个性化隐私水平（或成本）。我们假设平台的目标是优化统计数据的准确性，并且必须选择每个代理的隐私级别，以在i）激励更多参与和ii）为估计增加更少噪音之间进行权衡。我们提供了一个半封闭的形式表征的代理权重的最佳选择的平台在我们的模型的两个变体。在这两个模型中，我们确定了一个共同的非平凡的结构，在平台的最优解：一个实例特定数量的代理与最严格的隐私要求被汇集在一起，并给予相同的权重，而其余的代理的权重减少作为其隐私要求的强度的函数。我们还提供了算法的结果，如何找到最佳值的噪声参数所使用的平台和给予代理的权重。
英文摘要：
We study the problem faced by a data analyst or platform that wishes to collect private data from privacy-aware agents. To incentivize participation, in exchange for this data, the platform provides a service to the agents in the form of a statistic computed using all agents' submitted data. The agents decide whether to join the platform (and truthfully reveal their data) or not participate by considering both the privacy costs of joining and the benefit they get from obtaining the statistic. The platform must ensure the statistic is computed differentially privately and chooses a central level of noise to add to the computation, but can also induce personalized privacy levels (or costs) by giving different weights to different agents in the computation as a function of their heterogeneous privacy preferences (which are known to the platform). We assume the platform aims to optimize the accuracy of the statistic, and must pick the privacy level of each agent to trade-off between i) incentivizing more participation and ii) adding less noise to the estimate. We provide a semi-closed form characterization of the optimal choice of agent weights for the platform in two variants of our model. In both of these models, we identify a common nontrivial structure in the platform's optimal solution: an instance-specific number of agents with the least stringent privacy requirements are pooled together and given the same weight, while the weights of the remaining agents decrease as a function of the strength of their privacy requirement. We also provide algorithmic results on how to find the optimal value of the noise parameter used by the platform and of the weights given to the agents.
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