Information Contraction under $(\varepsilon,\delta)$-Differentially Private Mechanisms

Theshani Nuradha; Ian George; Christoph Hirche

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arXiv · 2601.16845

Information Contraction under $(\varepsilon,\delta)$-Differentially Private Mechanisms

Theshani Nuradha·Ian George·Christoph Hirche

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Abstract

The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard data-processing inequalities and strong data-processing inequalities (SDPI) are employed. Most of the previously known and even tight characterizations of contraction of information measures, including total variation distance, hockey-stick divergences, and $f$-divergences, are applicable for $(\varepsilon,0)$-local differential private (LDP) mechanisms. In this work, we derive both linear and non-linear strong data-processing inequalities for hockey-stick divergence and $f$-divergences that are valid for all $(\varepsilon,\delta)$-LDP mechanisms even when $\delta \neq 0$. Our results either generalize or improve the previously known bounds on the contraction of these distinguishability measures.

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Theshani Nuradha, Ian George, Christoph Hirche. 2026-01-23. Information Contraction under $(\varepsilon,\delta)$-Differentially Private Mechanisms. https://arxiv.org/abs/2601.16845

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