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arXiv · 1810.12518

Private Algorithms Can Always Be Extended

Christian Borgs·Jennifer Chayes·Adam Smith·Ilias Zadik
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Abstract

We consider the following fundamental question on $\epsilon$-differential privacy. Consider an arbitrary $\epsilon$-differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an $\epsilon'$-differentially private algorithm on the whole input space for some $\epsilon'$ comparable with $\epsilon$? In this note we answer affirmatively this question for $\epsilon'=2\epsilon$. Our result applies to every input metric space and space of possible outputs. This result originally appeared in a recent paper by the authors [BCSZ18]. We present a self-contained version in this note, in the hopes that it will be broadly useful.

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Christian Borgs, Jennifer Chayes, Adam Smith, Ilias Zadik. 2018-10-30. Private Algorithms Can Always Be Extended. https://arxiv.org/abs/1810.12518

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