To Shuffle or not to Shuffle: Auditing DP-SGD with Shuffling

Differentially Private Stochastic Gradient Descent (DP-SGD) is a popular method for training machine learning models with formal Differential Privacy (DP) guarantees. As DP-SGD processes the training data in batches, it uses Poisson sub-sampling to select batches at each step. However, due to computational and compatibility benefits, replacing sub-sampling with shuffling has become common practice. Yet, since tight theoretical guarantees for shuffling are currently unknown, prior work using shuffling reports DP guarantees as though Poisson sub-sampling was used. This prompts the need to verify whether this discrepancy is reflected in a gap between the theoretical guarantees from state-of-the-art models and the actual privacy leakage. To do so, we introduce a novel DP auditing procedure to analyze DP-SGD with shuffling. We show that state-of-the-art DP models trained with shuffling appreciably overestimated privacy guarantees (up to 4x). In the process, we assess the impact of several parameters, such as batch size, privacy budget, and threat model, on privacy leakage. Finally, we study two variations of the shuffling procedure found in the wild, which result in further privacy leakage. Overall, our work empirically attests to the risk of using shuffling instead of Poisson sub-sampling vis-\`a-vis the actual privacy leakage of DP-SGD.