The composition theorems of differential privacy (DP) allow data curators to combine different algorithms to obtain a new algorithm that continues to satisfy DP. However, new granularity notions (i.e., neighborhood definitions), data domains, and composition settings have appeared in the literature that the classical composition theorems do not cover. For instance, the parallel composition theorem does not apply to general granularity notions. This complicates the opportunity of composing DP mechanisms in new settings and obtaining accurate estimates of the incurred privacy loss after composition. To overcome these limitations, we study the composability of DP in a general framework and for any kind of data domain or neighborhood definition. We give a general composition theorem in both independent and adaptive versions and we provide analogous composition results for approximate, zero-concentrated, and Gaussian DP. Besides, we study the hypothesis needed to obtain the best composition bounds. Our theorems cover both parallel and sequential composition settings. Importantly, they also cover every setting in between, allowing us to compute the final privacy loss of a composition with greatly improved accuracy.

翻译：差分隐私的组合定理允许数据管理者组合不同算法，从而获得仍满足差分隐私的新算法。然而，文献中已出现经典组合定理未覆盖的新粒度概念（即邻域定义）、数据域和组合设置。例如，并行组合定理不适用于通用粒度概念。这增加了在新设置中组合差分隐私机制并准确评估组合后隐私损失的难度。为克服这些局限，我们在通用框架下研究差分隐私的组合性，并适用于任意类型的数据域或邻域定义。我们给出独立版本和自适应版本的通用组合定理，并为近似差分隐私、零集中差分隐私和高斯差分隐私提供相应组合结果。此外，我们研究了获得最佳组合边界所需的假设条件。我们的定理同时涵盖并行组合和串行组合设置。重要的是，它们也覆盖介于两者之间的所有设置，使我们能够以大幅提升的精度计算组合后的最终隐私损失。