Dobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy

Leonhard Grosse; Sara Saeidian; Tobias J. Oechtering; Mikael Skoglund

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arXiv · 2601.09498

Dobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy

Leonhard Grosse·Sara Saeidian·Tobias J. Oechtering·Mikael Skoglund

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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.

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Leonhard Grosse, Sara Saeidian, Tobias J. Oechtering, Mikael Skoglund. 2026-01-14. Dobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy. https://arxiv.org/abs/2601.09498

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