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 $\eta$-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 $(\varepsilon,\delta)$-DP with $\eta$-TV is closed under subsampling. The induced total variation of commonly used mechanisms are computed. Moreover, the notion of total variation of a mechanism is extended to the local privacy setting and privacy-utility tradeoffs are investigated. In particular, total variation distance and KL divergence are considered as utility functions and upper bounds are derived. Finally, the results are compared and connected to the (purely) locally differentially private setting.

翻译：本文考虑近似差分隐私框架，并通过引入"（隐私保护）机制的总变分"概念（记为$\eta$-TV）对其加以扩展。利用这一改进，推导出了精确的组合结果，并证明该结果显著优于未考虑总变分的差分隐私最优界。此外，研究表明$(\varepsilon,\delta)$-DP与$\eta$-TV在子抽样下保持封闭性。文中计算了常用机制诱导的总变分，并将机制总变分概念拓展至本地隐私设置，探究了隐私-效用权衡问题。特别地，以总变分距离和KL散度作为效用函数进行考量，推导了相应的上界。最后，将所得结果与纯本地差分隐私设置进行了比较和关联分析。