(Amplified) Banded Matrix Factorization: A unified approach to private training

Matrix factorization (MF) mechanisms for differential privacy (DP) have substantially improved the state-of-the-art in privacy-utility-computation tradeoffs for ML applications in a variety of scenarios, but in both the centralized and federated settings there remain instances where either MF cannot be easily applied, or other algorithms provide better tradeoffs (typically, as \epsilon becomes small).In this work, we show how MF can subsume prior state-of-the-art algorithms in both federated and centralized training settings, across all privacy budgets. The key technique throughout is the construction of MF mechanisms with banded matrices (lower-triangular matrices with at most \hat{b} nonzero bands including the main diagonal). For cross-device federated learning (FL), this enables multiple-participations with a relaxed device participation schema compatible with practical FL infrastructure (as demonstrated by a production deployment).