Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Kalinin, Nikita P.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403593978