Pufferfish privacy is a flexible generalization of differential privacy that allows to model arbitrary secrets and adversary's prior knowledge about the data. Unfortunately, designing general and tractable Pufferfish mechanisms that do not compromise utility is challenging. Furthermore, this framework does not provide the composition guarantees needed for a direct use in iterative machine learning algorithms. To mitigate these issues, we introduce a R\'enyi divergence-based variant of Pufferfish and show that it allows us to extend the applicability of the Pufferfish framework. We first generalize the Wasserstein mechanism to cover a wide range of noise distributions and introduce several ways to improve its utility. We also derive stronger guarantees against out-of-distribution adversaries. Finally, as an alternative to composition, we prove privacy amplification results for contractive noisy iterations and showcase the first use of Pufferfish in private convex optimization. A common ingredient underlying our results is the use and extension of shift reduction lemmas.

翻译：Pufferfish隐私是差分隐私的一种灵活推广，能够对任意秘密和攻击者对数据的先验知识进行建模。然而，设计既能保持效用又具有普适性和可操作性的Pufferfish机制颇具挑战。此外，该框架缺乏迭代机器学习算法直接使用所需的组合保证。为缓解这些问题，我们提出了基于Rényi散度的Pufferfish变体，并表明其能够扩展Pufferfish框架的适用性。我们首先推广了Wasserstein机制以覆盖广泛的噪声分布，并引入了多种提升其效用的方法。我们还针对分布外攻击者推导出更强的保障。最后，作为组合的替代方案，我们证明了压缩噪声迭代的隐私放大结果，并展示了Pufferfish在私有凸优化中的首次应用。上述结果的一个共同基础是位移缩减引理的使用与推广。