Differentially Private Continual Release with Relative Error

2026-08-20

AI Summary

研究在差分隐私下持续发布模型中通过允许相对误差减少MaxSum、MinSum、MaxSelect和MinSelect任务的误差，区分了非自适应与自适应输入流的影响。

Abstract

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.

Problem

• differential privacy
• continual release
• relative error
• non-adaptive
• adaptive

Innovation

• Differential Privacy
• Continual Release Model
• Relative Error
• Non-adaptive Streams
• Adaptive Streams