GPT Astra 关于差分隐私持续计数下界证明的阐述
An Exposition of GPT Astra's Proof of Lower Bound on DP Continual Counting
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中文总结 AI 辅助
本文详细阐述Astra关于差分隐私持续计数下界的证明，并指出存在更自然简单的证明路径，同时梳理了相关前期工作及其技术联系。
中文摘要 AI 辅助
本笔记的目标是，在我们理解的基础上，对 Harrison 和 Leeman（arXiv:2609.17650v01 和 arXiv:2609.17650v02）所展示的 Astra 关于差分隐私持续计数下界的证明给出一个详细的证明。我们认为存在一个更自然且更简单的证明，并希望本笔记能有助于这一努力。在 Harrison 和 Leeman 的初始预印本（arXiv:2609.17650v01）之前，Bairaktari 和 Larsen（arXiv:2607.00876）给出了一个优雅的证明，表明纯差分隐私和近似差分隐私持续计数的下界均为 Ω(log^{3/2}(n))，并在个人交流中告知我们，他们也有一个针对纯差分隐私持续计数的最优 Ω(log^{2}(n)) 下界证明。他们随后发表了他们的 Ω(log^{2}(n)) 下界，这现在是 Bairaktari、Dahl 和 Larsen 的联合工作（arXiv:2607.00876v3）。他们的新结果是对其近似差分隐私技术的优雅扩展。尽管这两个证明在技术上有所不同，但 Astra 的论证使用了 Bairaktari 和 Larsen 引入的相关树几何结构。
英文摘要
The goal of this note is to give a detailed proof, to the best of our understanding, of the recent presentation by Harrison and Leeman (arXiv:2609.17650v01 and arXiv:2609.17650v02) of the proof by Astra on the lower bound for differentially private continual counting. We believe a more natural and easy proof is possible and hope that this note will help in that effort. Prior to the initial preprint by Harrison and Leeman (arXiv:2609.17650v01), Bairaktari and Larsen (arXiv:2607.00876) gave an elegant proof to show a lower bound of $Ω(\log^{3/2}(n))$ for both pure and approximate-DP continual counting, and in personal communication had informed us that they have a proof of optimal $Ω(\log^{2}(n))$ for pure-differential private continual counting as well. They have subsequently published their $Ω(\log^{2}(n))$ bound, which is now a joint work of Bairaktari, Dahl, and Larsen (arXiv:2607.00876v3). Their new result is an elegant extension of their technique for approximate-differential privacy. Although the two proofs are technically different, the Astra argument uses related tree geometry introduced in Bairaktari and Larsen.
发表机构
- Rutgers University（罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。
