Total Variation with Differential Privacy: Tighter Composition and Asymptotic Bounds

Elena Ghazi, Ibrahim Issa

Abstract: The framework of approximate differential privacy is considered, and augmented by introducing the notion of "the total variation of a (privacy-preserving) mechanism" (denoted by η-TV). With this refinement, an exact composition result is derived, and shown to be significantly tighter than the optimal bounds for differential privacy (which do not consider the total variation). Furthermore, it is shown that (ε, δ)-DP with η-TV is closed under subsampling. Finally, the induced total variation of commonly used mechanisms are computed.