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 }^\u2032\\)-differentially private algorithm on the whole input space for some \\({\\epsilon }^\u2032\\) comparable with \\(\\epsilon\\)? In this note we answer affirmatively this question for \\({\\epsilon }^\u2032=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.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider the following fundamental question on -differential privacy. Consider an arbitrary -differentially private algorithm defined on a subset of the input space. Is it possible to extend it to an -differentially private algorithm on the whole input space for some comparable with ? In this note we answer affirmatively this question for . 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