提出最优的局部差分隐私采样方法，兼顾隐私与数据效用
Exactly Minimax-Optimal Locally Differentially Private Sampling
- 基于f散度定义隐私-效用权衡，构建极小极大最优框架
- 在有限与连续数据空间下均实现理论最优效用
- 适用于生成模型等需隐私保护的采样场景
在局部差分隐私下的采样问题近年来受到关注，尤其在生成模型中有潜在应用，但其隐私-效用权衡（PUT）的基础分析仍不完整。本文从极小极大角度定义了私有采样的基础隐私-效用权衡，以原始分布与采样分布间的f散度作为效用度量。在对数据分布施加一些温和条件下，我们刻画了有限与连续数据空间下的精确隐私-效用权衡，并提出了对所有f散度均全局最优的采样机制。数值实验表明，该机制在有限数据空间下具有理论最优效用，在连续数据空间下表现出更优的实证效用，优于现有基线方法。
原文摘要 · Abstract (English)
The sampling problem under local differential privacy has recently been studied with potential applications to generative models, but a fundamental analysis of its privacy-utility trade-off (PUT) remains incomplete. In this work, we define the fundamental PUT of private sampling in the minimax sense, using the f-divergence between original and sampling distributions as the utility measure. We characterize the exact PUT for both finite and continuous data spaces under some mild conditions on the data distributions, and propose sampling mechanisms that are universally optimal for all f-divergences. Our numerical experiments demonstrate the superiority of our mechanisms over baselines, in terms of theoretical utilities for finite data space and of empirical utilities for continuous data space.
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