Scaling up the Banded Matrix Factorization Mechanism for Large Scale Differentially Private ML

Correlated noise mechanisms such as DP Matrix Factorization (DP-MF) have proven to be effective alternatives to DP-SGD in large-epsilon few-epoch training regimes. Significant work has been done to find the best correlated noise strategies, and the current state-of-the-art approach is DP-BANDMF, which optimally balances the benefits of privacy amplification and noise correlation. Despite it's utility advantages, severe scalability limitations prevent this mechanism from handling large-scale training scenarios where the number of training iterations may exceed 10 4 and the number of model parameters may exceed 10 7 . In this work, we present techniques to scale up DP-BANDMF along these two dimensions, significantly extending it's reach and enabling it to handle settings with virtually any number of model parameters and training iterations, with negligible utility degradation.