arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2203.05481cs.LGcs.CRcs.DSstat.ML
收藏

差分隐私中的完全自适应组合

Fully Adaptive Composition in Differential Privacy

Carnegie Mellon University(卡内基梅隆大学);LinkedIn(领英)

Justin Whitehouse, Aaditya Ramdas, Ryan Rogers, Zhiwei Steven Wu

AI总结:

本文研究差分隐私中的完全自适应组合问题,通过利用鞅浓度的进展,构建了匹配先进组合速率的隐私过滤器和通用的隐私里程表,证明了完全自适应隐私几乎无损失即可获得。

摘要:

组合是差分隐私的一个关键特性。著名的先进组合定理允许对私有数据库的查询次数比基本隐私组合所允许的多二次方倍。然而,这些结果要求在交互数据之前固定所有算法的隐私参数。为了解决这个问题,Rogers等人引入了完全自适应组合,其中算法及其隐私参数都可以自适应地选择。他们定义了两个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,即隐私损失的时间一致界限。先进组合与现有的过滤器和里程表之间存在巨大差距。首先,现有的过滤器对被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,使其不切实际。我们构建了匹配先进组合速率(包括常数)的过滤器,尽管允许自适应选择隐私参数。在此过程中,我们还推导出了近似zCDP的隐私过滤器。我们还构建了几个通用的里程表族。这些里程表在任意预先选定的时间点,或在所有时间点同时,匹配先进组合的紧致性,仅差一个双对数因子。我们通过利用鞅浓度的进展获得了我们的结果。总之,我们表明完全自适应隐私几乎无损失即可获得。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑