Optimal Conversion From Rényi Differential Privacy to F-Differential Privacy

MCML Authors

Anneliese Riess

→ Group Julia Schnabel
 Computational Imaging and AI in Medicine

Julia Schnabel

Prof. Dr.

Core PI

Computational Imaging and AI in Medicine

Abstract

We prove the conjecture stated in Appendix F.3 of Zhu et al. (2022): among all conversion rules that map a R´ enyi Differential Privacy (RDP) profile τ →ρ(τ) to a valid hypothesis-testing trade-off f, the rule based on the intersection of single-order RDP privacy regions is optimal. This optimality holds simultaneously for all valid RDP profiles and for all Type I error levels α. Concretely, we show that in the space of trade-off functions, the tightest possible bound is fρ(·)(α) = supτ≥0.5 fτ,ρ(τ)(α): the pointwise maximum of the single-order bounds for each RDP privacy region. Our proof unifies and sharpens the insights of Balle et al. (2019), Asoodeh et al. (2021), and Zhu et al. (2022). Our analysis relies on a precise geometric characterization of the RDP privacy region, leveraging its convexity and the fact that its boundary is determined exclusively by Bernoulli mechanisms. Our results establish that the 'intersection-of-RDP-privacy-regions' rule is not only valid, but optimal: no other black-box conversion can uniformly dominate it in the Blackwell sense, marking the fundamental limit of what can be inferred about a mechanism’s privacy solely from its RDP guarantees.

inproceedings RGC+26

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ICML 2026

43rd International Conference on Machine Learning. Seoul, South Korea, Jul 06-11, 2026. To be published. Preprint available.

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Authors

A. Riess • J. F. Gomez • F. Calmon • J. A. Schnabel • G. Kaissis

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Links

URL GitHub

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Research Area

 C1 | Medicine