证明了采样高斯机制中噪声随采样率下降的猜想，完善了差分隐私理论。
Notes on Sampled Gaussian Mechanism
- 通过严格推导证明采样率越高，有效噪声越低
- 确认大采样率能实现更优的隐私与性能平衡
- 适合关注差分隐私理论严谨性的研究人员
本文证明了Räisä等在2024年论文中提出的近期猜想。该论文中的定理6.2指出，对于采样高斯机制——即采样与加性高斯噪声的组合——其有效噪声水平 $σ_{\text{eff}} = \frac{σ(q)}{q}$ 随采样率 $q$ 的增加而减小。因此，更高的采样率可带来更好的隐私-效用权衡。本文提供了对原论文中未解决的猜想6.3的严格证明，从而完整确立了定理6.2的成立。
原文摘要 · Abstract (English)
In these notes, we prove a recent conjecture posed in the paper by Räisä, O. et al. [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimization (2024)]. Theorem 6.2 of the paper asserts that for the Sampled Gaussian Mechanism - a composition of subsampling and additive Gaussian noise, the effective noise level, $σ_{\text{eff}} = \frac{σ(q)}{q}$, decreases as a function of the subsampling rate $q$. Consequently, larger subsampling rates are preferred for better privacy-utility trade-offs. Our notes provide a rigorous proof of Conjecture 6.3, which was left unresolved in the original paper, thereby completing the proof of Theorem 6.2.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。