The accuracy-first perspective of differential privacy addresses an important shortcoming by allowing a data analyst to adaptively adjust the quantitative privacy bound instead of sticking to a predetermined bound. Existing works on the accuracy-first perspective have neglected an important property of differential privacy known as post-processing immunity, which ensures that an adversary is not able to weaken the privacy guarantee by post-processing. We address this gap by determining which existing definitions in the accuracy-first perspective have post-processing immunity, and which do not. The only definition with post-processing immunity, pure ex-post privacy, lacks useful tools for practical problems, such as an ex-post analogue of the Gaussian mechanism, and an algorithm to check if accuracy on separate private validation set is high enough. To address this, we propose a new definition based on Rényi differential privacy that has post-processing immunity, and we develop basic theory and tools needed for practical applications. We demonstrate the practicality of our theory with applications to synthetic data generation and image classifier fine-tuning, where our algorithm successfully adjusts the privacy bound until an accuracy threshold is met on a private validation dataset.

翻译：差分隐私的精准优先视角通过允许数据分析师自适应调整量化隐私界限而非固守预设界限，解决了该领域一个重要缺陷。现有基于精准优先视角的研究忽视了差分隐私中称为后处理免疫性的重要特性——该特性确保攻击者无法通过后处理操作削弱隐私保障。我们通过判定精准优先视角下哪些现有定义具备后处理免疫性来填补这一空白。在具备后处理免疫性的定义中，唯一满足该特性的纯事后隐私缺乏实用问题所需的工具集，例如高斯机制的事后类比方法，以及验证独立私有验证集上精准度是否达标的算法。为此，我们提出一种基于Rényi差分隐私且具备后处理免疫性的新型定义，并开发了实际应用所需的基础理论与工具。通过合成数据生成与图像分类器微调等应用实例，我们验证了理论方法的实用性——在这些场景中，我们的算法能成功调整隐私界限直至私有验证数据集上的精确度阈值得到满足。