Abstract: 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 $\varepsilon=10.0$, our auditing procedure yields empirical estimates of $\varepsilon_{emp} = 7.21$ and $6.95$, respectively, on a 1,000-record sample and $\varepsilon_{emp} = 6.48$ 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 from https://github.com/spalabucr/bb-audit-dpsgd.