Composition theorems are general and powerful tools that facilitate privacy accounting across multiple data accesses from per-access privacy bounds. However they often result in weaker bounds compared with end-to-end analysis. Two popular tools that mitigate that are the exponential mechanism (or report noisy max) and the sparse vector technique. They were generalized in a couple of recent private selection/test frameworks, including the work by Liu and Talwar (STOC 2019), and Papernot and Steinke (ICLR 2022). In this work, we first present an alternative framework for private selection and testing with a simpler privacy proof and equally-good utility guarantee. Second, we observe that the private selection framework (both previous ones and ours) can be applied to improve the accuracy/confidence trade-off for many fundamental privacy-preserving data-analysis tasks, including query releasing, top-$k$ selection, and stable selection. Finally, for online settings, we apply the private testing to design a mechanism for adaptive query releasing, which improves the sample complexity dependence on the confidence parameter for the celebrated private multiplicative weights algorithm of Hardt and Rothblum (FOCS 2010).

翻译：组合定理是通用的强大工具，它通过每次访问的隐私界限来简化跨多次数据访问的隐私核算。然而，与端到端分析相比，它们通常会导致更弱的界限。缓解这一问题的两种常用工具是指数机制（或称含噪最大值报告）和稀疏向量技术。这两种工具在最近的一些私有选择/测试框架中得到了泛化，包括Liu和Talwar（STOC 2019）的工作，以及Papernot和Steinke（ICLR 2022）的工作。在本文中，我们首先提出一个替代性的私有选择与测试框架，该框架具有更简洁的隐私证明和同样良好的效用保证。其次，我们观察到私有选择框架（包括先前框架和我们的框架）可以应用于改进许多基础隐私保护数据分析任务的精度/置信度权衡，包括查询发布、top-$k$选择和稳定选择。最后，针对在线设置，我们应用私有测试设计了一种自适应查询发布机制，该机制改进了Hardt和Rothblum（FOCS 2010）著名的私有乘法权重算法在样本复杂度上对置信度参数的依赖关系。