$α$-Wasserstein Mechanism for Rényi Pufferfish Privacy
This work provides a new framework for privacy-preserving data analysis that improves utility over existing methods for a broad class of privacy definitions.
The paper introduces the α-Wasserstein mechanism for achieving Rényi Pufferfish Privacy with Laplace and Gaussian noise, demonstrating that it reduces noise power compared to the W∞-based approach while providing exact privacy guarantees without δ-approximations.
This paper introduces the $α$-Wasserstein mechanism for achieving Rényi Pufferfish Privacy using Laplace and Gaussian noise. By leveraging Hölder's inequality, we demonstrate that the scale parameter of the Laplace mechanism can be calibrated via an upper bound on the $W_α$ metric to satisfy $(α, ε)$-Rényi Pufferfish Privacy for $α\in (1, \infty]$. We show that at the limit $α= \infty$, this framework recovers the established $W_\infty$ mechanism for $ε$-pufferfish privacy. This result is subsequently extended to the exponential mechanism. Furthermore, we propose a $W_α$ mechanism for Gaussian noise for $α\in (1, \infty)$, demonstrating that it generalizes existing results within the Rényi Differential Privacy framework. Experimental evaluations reveal that our $α$-Wasserstein mechanism significantly reduces noise power compared to the conventional $W_\infty$-based approach, with the Gaussian mechanism providing superior utility over the Laplace mechanism. Notably, the mechanisms derived in this work achieve exact $(α, ε)$-Rényi Pufferfish Privacy without requiring additional relaxations, such as $δ$-approximations.