The framework of approximate differential privacy is considered, and augmented by leveraging 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 studied in the local privacy setting and privacy-utility tradeoffs are investigated. In particular, total variation distance and KL divergence are considered as utility functions and studied through the lens of contraction coefficients. Finally, the results are compared and connected to the locally differentially private setting.

翻译：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”（记为$\eta$-TV）的概念对其进行增强。基于此改进，推导出一个精确的组合结果，该结果显著优于不考虑总变分的差分隐私最优界。进一步证明，具有$\eta$-TV的$(\varepsilon,\delta)$-DP对子采样封闭。计算了常用机制诱导的总变分。此外，在本地隐私设置下研究了机制总变分的概念，并探讨了隐私-效用权衡。特别地，将总变分距离和KL散度作为效用函数，通过收缩系数的视角进行分析。最后，将所得结果与本地差分隐私设置进行比较和关联。