$α$-Wasserstein Mechanism for Rényi Pufferfish Privacy

2026-05-07

AI Summary

This work proposes the α-Wasserstein mechanism to enhance data utility while preserving Rényi Pufferfish privacy. It establishes the first unified framework for all α ∈ (1, ∞], generalizing both the W_∞ mechanism and Rényi differential privacy. By calibrating the scale of Laplace and Gaussian noise through an upper bound on the Wasserstein distance, the method achieves (α, ε)-Rényi Pufferfish privacy without requiring a δ relaxation. Leveraging Hölder’s inequality and an extension of the exponential mechanism, the theoretical analysis significantly reduces the required noise magnitude, with the Gaussian variant outperforming Laplace. Consequently, the approach substantially improves data utility under stringent privacy guarantees.

Abstract

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.

Problem

• Rényi Pufferfish Privacy
• Wasserstein mechanism
• Laplace noise
• Gaussian noise
• privacy-preserving mechanism

Innovation

• α-Wasserstein mechanism
• Rényi Pufferfish Privacy
• Gaussian noise
• Laplace mechanism
• Hölder's inequality