指数选择中的局部敏感性：失效模式与有效校准

中文摘要 AI 辅助

选择是从有限的公开候选范围中选取一个元素，以最大化依赖于数据集的得分的任务。在差分隐私（DP）中，指数机制（EM）会根据全局敏感性校准温度来采样候选。本文研究在私有选择中，依赖于数据集的敏感性何时可以安全地替代全局敏感性。我们提出三种有效方法：第一，局部敏感性的私有高概率上界可产生近似差分隐私，该方法可扩展至有限的高阶敏感性层次；第二，我们的提议-测试-发布（PTR）变体在有限的公开网格中私有搜索温度尺度，而非预先固定；第三，平滑敏感性支持多种设计，与候选无关的平滑几何构造可生成在局部衰减框架下可容许的敏感性包络，任何可容许包络都能保证隐私，此外，单独的对数变换利用平滑敏感性生成平滑的候选得分函数，具有全局敏感性可控、保留原始效用得分最大化者（即最大化效用的候选）的优势，两种设计均产生与范围无关的纯差分隐私。除此之外，我们还给出两种使用平滑敏感性的近似差分隐私私有选择器：一种是根据候选范围和隐私参数校准平滑敏感性的直接指数机制（EM），其与理论下界的差异仅为某个常数因子；另一种是通过分析平滑性的对数变换使用私有平滑上尺度的选择器。对于每个提出的机制，我们在其规定条件下推导了高概率后悔界。

英文摘要

Selection is a task that chooses one element from a finite public candidate range to maximize a data-dependent score. In differential privacy (DP), the exponential mechanism (EM) samples a candidate at a temperature calibrated to the global sensitivity. In this paper, we study when dataset-dependent sensitivity can safely replace global sensitivity in private selection. We propose three valid approaches. First, a private, high-probability upper bound on local sensitivity yields approximate DP, and the method extends to finite higher-order sensitivity hierarchies. Second, our Propose-Test-Release (PTR) variant privately searches a finite public grid for a temperature scale rather than fixing it in advance. Third, smooth sensitivity supports several designs. A candidate-independent smooth geometric construction produces a sensitivity envelope that is admissible under the local dampening framework, which privacy is guaranteed for any admissible envelope. Additionally, a separate logarithmic transformation utilizes smooth sensitivity to produce a smoothed candidate score function with advantages: having controlled global sensitivity, and preserving the maximizers of the original utility score, i.e., candidates maximizing the utility. Both of the designs yield range-independent pure DP. Besides that, we also give two approximate DP private selectors using smooth sensitivity: a direct EM with smooth sensitivity calibrated to the candidate range and privacy parameters that matches a theoretical lower bound up to some constant factor, and one using a privatized smooth upper scale by analyzing the logarithmic transform of the smoothness. For every proposed mechanism, we derive a high-probability regret bound under its stated conditions.

发表机构

• University of Texas at San Antonio（圣安东尼奥德克萨斯大学）
• University of Virginia（弗吉尼亚大学）

机构由 AI 辅助整理，请以论文原文为准。