Tetsuya Sato · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.25636 · cited by 0 works (OpenAlex) · open-access PDF
Differential Privacy (DP) डेटाबेस की गोपनीयता गारंटी का मूल्यांकन करने के लिए डिज़ाइन किया गया है। Rényi Differential Privacy (RDP) DP का एक महत्वपूर्ण संस्करण है जो मशीन सीखने एल्गोरिथ्म के सख्त मूल्यांकन देता है। इन सूत्रों को समझना आसान है, लेकिन वास्तविक डेटाबेस के लिए गोपनीयता का मूल्यांकन जटिल है। डेटाबेस में एक छोटा सा परिवर्तन भी अपनी गोपनीयता को तोड़ सकता है, और DP और RDP के मूल्यांकन स्वयं जटिल हैं। विशेष रूप से, हाल के अध्ययनों में RDP मूल्यांकन बहुत मुश्किल हो गए हैं। इसलिए, उनके औपचारिक सत्यापन को एक दशक से अधिक के लिए अध्ययन किया गया है। इस दस्तावे
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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