[论文解读] Fully Adaptive Composition in Differential Privacy

Justin Whitehouse, Aaditya Ramdas+2 more|arXiv (Cornell University)|Mar 10, 2022

Privacy-Preserving Technologies in Data被引用 5

一句话总结

本文提出了隐私过滤器和计数器，用于完全自适应的差分隐私组合，其渐近隐私边界与高级组合方法相同，包括紧致常数，即使在自适应选择隐私参数的情况下也成立。通过利用鞅集中不等式，作者构建的过滤器达到了与高级组合方法相同的速率，计数器则在双重对数因子范围内最优，从而实现了低开销的实际自适应隐私会计。

ABSTRACT

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.

研究动机与目标

• 弥合高级组合与现有隐私过滤器/计数器在完全自适应差分隐私中的差距。
• 在自适应选择隐私参数的情况下，构建与高级组合方法隐私边界（包括常数）相匹配的隐私过滤器。
• 设计在任意或所有时间点上紧致的通用隐私计数器族，误差控制在双重对数因子范围内。
• 通过减少阻碍先前方法实用化的巨大常数，实现实际可行的自适应隐私会计。

提出的方法

• 利用鞅集中不等式推导自适应组合中隐私损失的紧致边界。
• 构建隐私过滤器，确保即使在自适应选择隐私参数的情况下，整体隐私预算仍被保留。
• 开发隐私计数器，提供累积隐私损失的时间统一、高概率上界。
• 基于隐私损失随机变量和条件期望提出新颖的分析框架，以推导紧致边界。
• 应用zCDP（零集中差分隐私）的结果，构建近似zCDP的过滤器。
• 优化计数器序列，使其在预设时间点或所有时间步上达到紧致，最小化高估。

实验结果

研究问题

• RQ1 能否为完全自适应组合构建隐私过滤器，使其与高级组合的隐私边界（包括常数）相匹配？
• RQ2 能否设计在自适应组合中任意或所有时间点上紧致的隐私计数器，误差控制在小的对数因子范围内？
• RQ3 如何减少现有过滤器和计数器中的巨大常数，以使其具有实际可用性？
• RQ4 当隐私参数自适应选择时，能否保持高级组合的理论保证？
• RQ5 是否可能实现完全自适应组合，且隐私效率损失最小？

主要发现

• 所提出的隐私过滤器即使在完全自适应选择隐私参数的情况下，也能达到与高级组合相同的渐近隐私边界，包括匹配的常数。
• 隐私计数器在任一预设时间点上的紧致性误差控制在双重对数因子范围内，且可针对不同隐私目标进行优化。
• 作者构建了近似zCDP的隐私过滤器，扩展了其框架的适用范围。
• 隐私损失边界通过鞅集中不等式推导，实现了对累积隐私损失的时间统一控制。
• 结果表明，差分隐私中的完全自适应几乎不会造成隐私效率损失，使其在理论上严谨且在实践中可行。