Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. They defined two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the rates of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. En route we also derive a privacy filter for approximate zCDP. We also construct several general families of odometers. These odometers match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging advances in martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss.

翻译：组合是差分隐私的一个关键特性。著名的进阶组合定理允许对私有数据库进行比基本隐私组合所允许的多四次方的查询。然而，这些结果要求所有算法的隐私参数在与数据交互之前就已固定。为解决此问题，Rogers等人引入了完全自适应组合，其中算法及其隐私参数均可自适应选择。他们定义了两种概率对象来衡量自适应组合中的隐私：隐私过滤器，为组合交互提供差分隐私保证；以及隐私里程表，对隐私损失进行时间统一的有界控制。当前进阶组合与现有过滤器及里程表之间存在显著差距。首先，现有过滤器对组合的算法施加了更强的假设。其次，这些里程表和过滤器存在较大的常数，导致其不实用。我们构建了与进阶组合（包括常数）匹配的过滤器，尽管允许隐私参数自适应选择。在此过程中，我们还推导出近似的zCDP隐私过滤器。同时，我们构建了几个通用家族式里程表。这些里程表在任意预选时间点与进阶组合的紧致性相匹配，或在所有时间点同时匹配（至多相差一个双对数因子）。我们通过利用鞅集中度的进展获得了这些结果。总之，我们证明了完全自适应隐私几乎可以无损耗地实现。