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Pufferfish privacy is a flexible generalization of differential privacy thatallows to model arbitrary secrets and adversary's prior knowledge about thedata. Unfortunately, designing general and tractable Pufferfish mechanisms thatdo not compromise utility is challenging. Furthermore, this framework does notprovide the composition guarantees needed for a direct use in iterative machinelearning algorithms. To mitigate these issues, we introduce a R\'enyidivergence-based variant of Pufferfish and show that it allows us to extend theapplicability of the Pufferfish framework. We first generalize the Wassersteinmechanism to cover a wide range of noise distributions and introduce severalways to improve its utility. We also derive stronger guarantees againstout-of-distribution adversaries. Finally, as an alternative to composition, weprove privacy amplification results for contractive noisy iterations andshowcase the first use of Pufferfish in private convex optimization. A commoningredient underlying our results is the use and extension of shift reductionlemmas.

R\'enyi Pufferfish Privacy: General Additive Noise Mechanisms and Privacy Amplification by Iteration