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

Part of International Conference on Representation Learning 2025 (ICLR 2025) Conference

Bibtex Paper Supplemental

Authors

Ryan McKenna

Abstract

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.