Abstract:We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition recovers local differential privacy (LDP) for $c\to 0$. We derive achievable bounds on contraction in terms of a kernels PML guarantees, and provide mechanism constructions that achieve the presented bounds. Further, we extend the results to general $f$-divergences by an application of Binette's inequality. Our analysis yields tighter bounds for mechanisms satisfying LDP and extends beyond the LDP regime to any discrete kernel.
From: Leonhard Grosse [view email]
[v1]
Wed, 14 Jan 2026 14:03:42 UTC (201 KB)
[v2]
Thu, 2 Jul 2026 15:19:50 UTC (200 KB)
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