Data is an increasingly vital component of decision making processes across industries. However, data access raises privacy concerns motivating the need for privacy-preserving techniques such as differential privacy. Data markets provide a means to enable wider access as well as determine the appropriate privacy-utility trade-off. Existing data market frameworks either require a trusted third party to perform computationally expensive valuations or are unable to capture the combinatorial nature of data value and do not endogenously model the effect of differential privacy. This paper addresses these shortcomings by proposing a valuation mechanism based on the Wasserstein distance for differentially-private data, and corresponding procurement mechanisms by leveraging incentive mechanism design theory, for task-agnostic data procurement, and task-specific procurement co-optimisation. The mechanisms are reformulated into tractable mixed-integer second-order cone programs, which are validated with numerical studies.

翻译：数据正日益成为各行业决策过程中的关键要素。然而，数据访问引发了隐私担忧，这推动了对差分隐私等隐私保护技术的需求。数据市场为扩大数据访问范围及确定合适的隐私-效用权衡提供了途径。现有数据市场框架要么需要可信第三方执行计算成本高昂的估值，要么无法捕捉数据价值的组合特性，且未能内生地建模差分隐私的影响。本文通过提出基于Wasserstein距离的差分隐私数据估值机制，并借助激励机制设计理论构建相应的采购机制——包括任务无关数据采购和任务特定采购协同优化——来解决这些缺陷。这些机制被重构为可处理的混合整数二阶锥规划问题，并通过数值研究进行了验证。