Tetsuya Sato · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.25636 · cited by 0 works (OpenAlex) · open-access PDF
La confidentialité différentielle (DP) est une définition standard d'or de la confidentialité conçue pour évaluer la garantie de confidentialité des bases de données. La confidentialité différentielle de Rényi (RDP) est une variante importante de la DP qui donne des évaluations étroites des algorithmes d'apprentissage automatique. Ces formulations sont faciles à comprendre, mais l'évaluation de la confidentialité pour les bases de données réelles est compliquée. Même un petit changement dans la base de données peut briser sa confidentialité et les évaluations de DP et de RDP elles-mêmes sont compliquées. En particulier, les évaluations de RDP dans les études récentes sont devenues beaucoup plus difficiles. Par conséquent, leur vérification formelle a été étudi
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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