Tetsuya Sato · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.25636 · cited by 0 works (OpenAlex) · open-access PDF
A privacidade diferencial (DP) é uma definição padrão de ouro de privacidade projetada para avaliar a garantia de privacidade de bancos de dados. A privacidade diferencial de Rényi (RDP) é uma variante importante da DP que dá avaliações apertadas de algoritmos de aprendizagem de máquina. Essas formulações são fáceis de entender, mas a avaliação da privacidade para bancos de dados reais é complicada. Mesmo uma pequena mudança na base de dados pode quebrar sua privacidade, e as avaliações de DP e RDP em si são complicadas. Em particular, as avaliações RDP em estudos recentes tornaram-se muito mais difíceis. Portanto, a verificação formal delas tem sido estudada por mais de uma década. Neste artigo, propomos uma biblioteca Isabelle/HOL para formalizar a privacidade diferencial de
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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