差分隐私下带相对误差的持续发布
Differentially Private Continual Release with Relative Error
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中文总结 AI 辅助
该研究针对差分隐私下持续发布模型的四类任务，证明非自适应输入流下引入相对误差可大幅降低误差，自适应流下仅选最小累计和属性任务误差大，其余任务仍可保小误差，补充了匹配下界。
中文摘要 AI 辅助
本研究在差分隐私框架下，针对持续发布模型中的多个基础任务展开研究，包括MaxSum（最大和）、MinSum（最小和）、MaxSelect（最大选择）与MinSelect（最小选择）。已有研究表明，这类任务的任何算法都必然存在较大的纯加性误差。我们证明，若允许相对误差项，且输入流为非自适应生成时，误差可大幅降低；但当输入数据记录可自适应选择时，我们证明，选择累计和最小的属性这一任务必然存在较大误差，而其他任务仍可达到较小的误差界。这揭示了非自适应流与自适应流之间的显著差异，同时我们还为所提算法补充了几乎匹配的下界。
英文摘要
This work investigates several fundamental tasks, including $\mathsf{MaxSum}$, $\mathsf{MinSum}$, $\mathsf{MaxSelect}$, and $\mathsf{MinSelect}$, in the continual release model under differential privacy. Previous research has demonstrated that any algorithm for these tasks must admit a large purely additive error. We show that the error can be substantially reduced if a relative error term is allowed, provided that the input stream is generated non-adaptively. However, when input data records can be selected adaptively, we prove that a large error is inevitable for the task of selecting an attribute with a small cumulative sum, whereas small error bounds remain achievable for other tasks. This reveals a significant separation between non-adaptive and adaptive streams. We also complement our algorithms with nearly matching lower bounds.
