Task-aware Kernel Stein certificates for R\'{e}nyi differential privacy

arXiv:2610.23798v1 Announce Type: cross Abstract: R\`enyi differential privacy, based on R\`enyi divergence, has become a notion of choice for privacy guarantees. However, outside the Gaussian setting, R\`enyi divergence can be difficult to compute. In particular, R\`enyi differential privacy guarantees that exploit task-specific information, as in R\`enyi Pufferfish privacy, can be challenging. Here we use kernel Stein discrepancies based on escort distributions to provide certificates for R\`enyi differential privacy. By designing the kernel to focus on the relevant privacy directions, we also derive task-aware privacy certificates. We provide exact identities for Gaussian and Laplace mechanisms and bounds for exponential mechanisms, with separate task-aware guarantees. A real data set example illustrates how the protected comparison set and the released subspace jointly determine the resulting certificates.