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arXiv · 2409.04636

Notes on Sampled Gaussian Mechanism

Nikita P. Kalinin
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Abstract

In these notes, we prove a recent conjecture posed in the paper by R\"ais\"a, 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, $\sigma_{\text{eff}} = \frac{\sigma(q)}{q}$, 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.

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Nikita P. Kalinin. 2024-09-06. Notes on Sampled Gaussian Mechanism. https://arxiv.org/abs/2409.04636

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