Papers › Nearly Tight Black-Box Auditing of Differentially Private Machine Learning

Nearly Tight Black-Box Auditing of Differentially Private Machine Learning

23 May 2024arXiv:2405.14106archive 2025-07-28

Meenatchi Sundaram Muthu Selva Annamalai, Emiliano De Cristofaro

This paper presents an auditing procedure for the Differentially Private Stochastic Gradient Descent (DP-SGD) algorithm in the black-box threat model that is substantially tighter than prior work. The main intuition is to craft worst-case initial model parameters, as DP-SGD's privacy analysis is agnostic to the choice of the initial model parameters. For models trained on MNIST and CIFAR-10 at theoretical ε=10.0, our auditing procedure yields empirical estimates of εₑₘₚ = 7.21 and $6.95$, respectively, on a 1,000-record sample and εₑₘₚ= 6.48 and $4.96$ on the full datasets. By contrast, previous audits were only (relatively) tight in stronger white-box models, where the adversary can access the model's inner parameters and insert arbitrary gradients. Overall, our auditing procedure can offer valuable insight into how the privacy analysis of DP-SGD could be improved and detect bugs and DP violations in real-world implementations. The source code needed to reproduce our experiments is available at https://github.com/spalabucr/bb-audit-dpsgd.

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