Tetsuya Sato · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.25636 · cited by 0 works (OpenAlex) · open-access PDF
La privacidad diferencial (DP) es una definición estándar de oro de la privacidad diseñada para evaluar la garantía de privacidad de las bases de datos. La privacidad diferencial de Rényi (RDP) es una variante importante de la DP que da evaluaciones estrictas de los algoritmos de aprendizaje automático. Estas formulaciones son fáciles de entender, pero la evaluación de la privacidad para las bases de datos reales es complicada. Incluso un pequeño cambio en la base de datos puede romper su privacidad, y las evaluaciones de DP y RDP en sí son complicadas. En particular, las evaluaciones de RDP en estudios recientes se han vuelto mucho más difíciles. Por lo tanto, la verificación formal de ellas ha sido estudiada durante más de una década. En este artículo, proponemos una biblioteca Isabelle/HOL para formalizar la privacidad
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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