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 be more than $10^4$ 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 effectively handle settings with over $10^6$ training iterations and $10^9$ model parameters, with no utility degradation at smaller scales.