# Optimal conversion from R'enyi Differential Privacy to f-Differential Privacy

arXiv: https://arxiv.org/abs/2602.04562 · HTML: https://mlsanity.com/paper/2602.04562/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2026.

## Built on by (most cited first, 3 of 3)

- [Tight Auditing of Differential Privacy in MST and AIM](https://mlsanity.com/paper/2604.18352/) (2026)
- [Can R'enyi Accountants Beat Lossless Accountants for DP-SGD?](https://mlsanity.com/paper/2610.17120/) (2026)
- [Tight End-to-End Accounting for Differentially Private Synthetic Data](https://mlsanity.com/paper/2610.17249/) (2026)

## Abstract (arXiv)

We prove the conjecture stated in Appendix F.3 of citetzhu2022optimalaccountingdifferentialprivacy: among all conversion rules that map a R'enyi 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 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 citetballe2019hypothesistestinginterpretationsrenyi, citetasoodeh2021variantsdifferentialprivacylossless, and citetzhu2022optimalaccountingdifferentialprivacy. 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 enquoteintersection-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.