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arXiv 2603.09167cs.CR
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具有Rényi差分隐私的最优分区选择

Optimal partition selection with Rényi differential privacy

Google(谷歌);Google Research(谷歌研究)

Charlie Harrison, Pasin Manurangsi

AI总结:

本文提出了一种在Rényi差分隐私下优化分区选择的算法,通过改进Gaussian机制提升性能,同时揭示了支持频率发布算法的固有成本。

摘要:

在隐私数据分析中,一个常见问题是在可能无限的集合中选择分区(例如GROUP BY操作中的键)。这里的挑战在于在满足差分隐私约束的情况下最大化发布的分区集。之前的工作[Desfontaines等人,PoPETS 2022]提出了当每个用户仅提交一个分区时的最优(ε,δ)-DP算法。我们扩展了这种方法,以在δ-近似(α,ε)-Rényi差分隐私(RDP)下找到最优算法,这允许在组合下进行更紧密的分析。受用户提交多个分区情况下一般最优性结果不存在的启发,我们提出了一个扩展的最优算法,该算法针对L²有界加权分区选择进行了优化,可以作为Gaussian机制的改进,只要分区频率不需要时。我们展示了我们的基本原语可以轻松地插入到最先进的分区选择算法(PolicyGaussian从[Gopi等人,ICML 2020]和MAD2R从[Chen等人,ICML 2025])中,从而在并行和顺序自适应算法中提高性能。最后,我们展示了支持发布频率以及分区的算法存在固有的成本。具体来说,我们提出了一个基本的最优近似RDP算法的概念,用于分区选择,使用加性噪声,并展示了对于此问题,加性噪声机制和非加性噪声机制之间存在数值差异。

英文摘要:

A common problem in private data analysis is the partition selection problem, where each user holds a set of partitions (e.g. keys in a GROUP BY operation) from a possibly unbounded set. The challenge here is in maximizing the set of released partitions while respecting a differential privacy constraint. Previous work [Desfontaines et al., PoPETS 2022] presented an optimal $(\varepsilon, δ)$-DP algorithm when each user submits only a single partition. We generalize this approach to find the optimal algorithm under $δ$-approximate $(α, \varepsilon)$-Rényi differential privacy (RDP), which allows much tighter analysis under composition. Motivated by the non-existence of a general optimality result in the case where users submit multiple partitions each, we present an extension of our optimal algorithm tuned for $L^2$ bounded weighted partition selection which can be used as a drop-in improvement over the Gaussian mechanism any time the partition frequency is not also needed. We show that our primitive can be easily plugged into state of the art partition selection algorithms (PolicyGaussian from [Gopi et al., ICML 2020] and MAD2R from [Chen et al., ICML 2025]), improving performance both for parallel and sequential adaptive algorithms. Finally, we show that there is an inherent cost to algorithms which do support releasing the frequency as well as the partitions. Specifically, we formulate a basic notion of optimal approximate RDP algorithm for partition selection using additive noise, and show that there is a numerical separation between additive and non-additive noise mechanisms for this problem.

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。

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