Optimal conversion from Rényi Differential Privacy to $f$-Differential Privacy
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914615179345920 |
|---|---|
| author | Riess, Anneliese Gomez, Juan Felipe Calmon, Flavio du Pin Schnabel, Julia Anne Kaissis, Georgios |
| author_facet | Riess, Anneliese Gomez, Juan Felipe Calmon, Flavio du Pin Schnabel, Julia Anne Kaissis, Georgios |
| contents | We prove the conjecture stated in Appendix F.3 of \citet{zhu2022optimalaccountingdifferentialprivacy}: among all conversion rules that map a Rényi Differential Privacy (RDP) profile $τ\mapsto ρ(τ)$ 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 $f_{ρ(\cdot)}(α) = \sup_{τ\geq 0.5} f_{τ,ρ(τ)}(α)$: the pointwise maximum of the single-order bounds for each RDP privacy region.
Our proof unifies and sharpens the insights of \citet{balle2019hypothesistestinginterpretationsrenyi}, \citet{asoodeh2021variantsdifferentialprivacylossless}, and \citet{zhu2022optimalaccountingdifferentialprivacy}.
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 \enquote{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04562 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal conversion from Rényi Differential Privacy to $f$-Differential Privacy Riess, Anneliese Gomez, Juan Felipe Calmon, Flavio du Pin Schnabel, Julia Anne Kaissis, Georgios Cryptography and Security We prove the conjecture stated in Appendix F.3 of \citet{zhu2022optimalaccountingdifferentialprivacy}: among all conversion rules that map a Rényi Differential Privacy (RDP) profile $τ\mapsto ρ(τ)$ 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 $f_{ρ(\cdot)}(α) = \sup_{τ\geq 0.5} f_{τ,ρ(τ)}(α)$: the pointwise maximum of the single-order bounds for each RDP privacy region. Our proof unifies and sharpens the insights of \citet{balle2019hypothesistestinginterpretationsrenyi}, \citet{asoodeh2021variantsdifferentialprivacylossless}, and \citet{zhu2022optimalaccountingdifferentialprivacy}. 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 \enquote{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. |
| title | Optimal conversion from Rényi Differential Privacy to $f$-Differential Privacy |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2602.04562 |