Traditional approaches to differential privacy assume a fixed privacy requirement $\epsilon$ for a computation, and attempt to maximize the accuracy of the computation subject to the privacy constraint. As differential privacy is increasingly deployed in practical settings, it may often be that there is instead a fixed accuracy requirement for a given computation and the data analyst would like to maximize the privacy of the computation subject to the accuracy constraint. This raises the question of how to find and run a maximally private empirical risk minimizer subject to a given accuracy requirement. We propose a general "noise reduction" framework that can apply to a variety of private empirical risk minimization (ERM) algorithms, using them to "search" the space of privacy levels to find the empirically strongest one that meets the accuracy constraint, incurring only logarithmic overhead in the number of privacy levels searched. The privacy analysis of our algorithm leads naturally to a version of differential privacy where the privacy parameters are dependent on the data, which we term ex-post privacy, and which is related to the recently introduced notion of privacy odometers. We also give an ex-post privacy analysis of the classical AboveThreshold privacy tool, modifying it to allow for queries chosen depending on the database. Finally, we apply our approach to two common objectives, regularized linear and logistic regression, and empirically compare our noise reduction methods to (i) inverting the theoretical utility guarantees of standard private ERM algorithms and (ii) a stronger, empirical baseline based on binary search.

本文提出了一种名为噪声约简框架的通用方法，能够应用于各种私有经验风险最小化(ERM)算法，使用它们来“搜索”隐私级别的空间，以找到在满足准确性约束下最强的隐私级别，并仅产生对搜索的隐私级别数量的对数开销。

优先考虑准确度：选择不泄露隐私的差分隐私阈值以满足准确度约束的ERM