Individual Privacy Accounting for Differentially Private Stochastic Gradient Descent

TL;DR

This paper introduces a method to assess individual privacy guarantees in differentially private deep learning models trained with DP-SGD, revealing that many examples have stronger privacy than worst-case bounds and that privacy correlates with training loss and utility.

Contribution

It proposes output-specific privacy accounting for individual data points in DP-SGD and develops an efficient algorithm to analyze privacy at the example level.

Findings

Most data points have stronger privacy guarantees than the worst-case bound.

Privacy guarantees are correlated with training loss and model utility.

Underserved groups in utility also experience weaker privacy guarantees.

Abstract

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 output-specific $(\varepsilon,\delta)$-DP to characterize privacy guarantees for individual examples when releasing models trained by DP-SGD. We also design an efficient algorithm to investigate individual privacy 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 simultaneously experience weaker privacy guarantees. For example, on CIFAR-10, the average $\varepsilon$ of the class with the lowest test accuracy is 44.2\% higher than that of the class with the highest accuracy.