Tetsuya Sato · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.25636 · cited by 0 works (OpenAlex) · open-access PDF
差异隐私(DP)是一个金标准的隐私定义,旨在评估数据库的隐私保障。Rényi差异隐私(RDP)是DP的一种重要变体,它提供了对机器学习算法的严格评估。这些公式很容易理解,但对实际数据库的隐私评估是复杂的。即使是数据库中的一些变化也可能会破坏其隐私,而且对DP和RDP本身的评估是复杂的。特别是,近期研究中的RDP评估变得更加困难。因此,对它们的正式验证已经研究了十多年。在这篇论文中,我们提出了一个伊莎贝尔/HOL图书馆,用来正式化Rényi差异隐私的一般设置。我们首先正式化RDP进行连续分布。作为技术基础,我们正式化了几种圆形函数的
Machine translation (Meta M2M100); the English original follows.
Differential privacy (DP) is a gold-standard definition of privacy designed to evaluate the privacy guarantee of databases. Rényi differential privacy (RDP) is an important variant of DP that gives tight evaluations of machine learning algorithms. These formulations are easy to understand, but evaluating privacy for actual databases is complicated. Even a small change in the database can break its privacy, and evaluations of DP and RDP themselves are complicated. In particular, RDP evaluations in recent studies have become much harder. Therefore, formal verification of them has been studied for over a decade. In this paper, we propose an Isabelle/HOL library for formalizing Rényi differential privacy in a general setting. We first formalize RDP for continuous distributions. As a technical basis, we formalize several properties of convex functions and $f$-divergences for nonnegative convex functions. We formalize basic properties of RDP, conversion laws from RDP to DP, the moment accountants in DP, and the Gaussian mechanism and its RDP. Finally, we discuss the stochastic gradient descent mechanism with Gaussian noise and formalize a rough evaluation of its RDP and DP.
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Topics: Differential privacy, Computer science, Regular polygon, Gaussian, Information privacy, Differential (mechanical device)
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