Generalized Private Selection and Testing with High Confidence

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, generalized in a recent private selection framework by Liu and Talwar (STOC 2019). In this work, we propose a flexible framework of private selection and testing that generalizes the one proposed by Liu and Talwar, supporting a wide range of applications. We apply our framework to solve several fundamental tasks, including query releasing, top-$k$ selection, and stable selection, with improved confidence-accuracy tradeoffs. Additionally, for online settings, we apply our 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).