It's Our Loss: No Privacy Amplification for Hidden State DP-SGD With Non-Convex Loss

Differentially Private Stochastic Gradient Descent (DP-SGD) is a popular iterative algorithm used to train machine learning models while formally guaranteeing the privacy of users. However, the privacy analysis of DP-SGD makes the unrealistic assumption that all intermediate iterates (aka internal state) of the algorithm are released since, in practice, only the final trained model, i.e., the final iterate of the algorithm is released. In this hidden state setting, prior work has provided tighter analyses, albeit only when the loss function is constrained, e.g., strongly convex and smooth or linear. On the other hand, the privacy leakage observed empirically from hidden state DP-SGD, even when using non-convex loss functions, suggests that there is in fact a gap between the theoretical privacy analysis and the privacy guarantees achieved in practice. Therefore, it remains an open question whether hidden state privacy amplification for DP-SGD is possible for all (possibly non-convex) loss functions in general.