Individual Privacy Accounting for Differentially Private Stochastic Gradient Descent

Differentially private stochastic gradient descent (DP-SGD) is the workhorse algorithm for recent advances in private deep learning. It provides a single privacy guarantee to all datapoints in the dataset. We propose an efficient algorithm to compute privacy guarantees for individual examples when releasing models trained by DP-SGD. We use our algorithm to investigate individual privacy parameters across a number of datasets. We find that most examples enjoy stronger privacy guarantees than the worst-case bound. We further discover that the training loss and the privacy parameter of an example are well-correlated. This implies groups that are underserved in terms of model utility are simultaneously underserved in terms of privacy guarantee. For example, on CIFAR-10, the average $\epsilon$ of the class with the lowest test accuracy is 26.3% higher than that of the class with the highest accuracy. We also run membership inference attacks to show this reflects disparate empirical privacy risks.