Optimal Rates for Differentially Private Hypothesis Testing with E-values

Computer Science > Cryptography and Security [Submitted on 27 May 2026] Optimal Rates for Differentially Private Hypothesis Testing with E-values Ben Jacobsen, Tomas Gonzales, Gavin Brown, Kassem Fawaz, Aaditya Ramdas E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions \mathbb{P} and \mathbb{Q}, what is the maximum achievable e-power when testing X\sim \mathbb{P}^n against X\sim\mathbb{Q}^n with e-values that satisfy \varepsilon-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and the analyst chooses when to halt, we give matching upper and lower bounds on the stopping times of any private e-process. Numerical experiments confirm the practicality of our algorithms, which require less data than the recently proposed DP-SPRT across a range of sequential testing problems and privacy levels. Comments: 28 pages, 2 figures Subjects: Cryptography and Security (cs.CR); Data Structures and Algorithms (cs.DS); Information Theory (cs.IT); Machine Learning (cs.LG) Cite as: arXiv:2605.28952 [cs.CR]   (or arXiv:2605.28952v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2605.28952 Focus to learn more Submission history From: Ben Jacobsen [view email] [v1] Wed, 27 May 2026 18:00:13 UTC (595 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-05 Change to browse by: cs cs.DS cs.IT cs.LG math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)