Learning Rate Scheduling with Matrix Factorization for Private Training
This work addresses the problem of enhancing private training efficiency for machine learning practitioners by providing a schedule-aware factorization, though it is incremental as it builds on existing correlated noise techniques.
The paper tackles the problem of improving accuracy in differentially private model training by addressing the gap between theoretical work on correlated noise with constant learning rates and practical use of learning rate schedules. It proposes a learning-rate-aware matrix factorization that outperforms prior methods, with experiments on CIFAR-10 and IMDB datasets confirming accuracy improvements.
We study differentially private model training with stochastic gradient descent under learning rate scheduling and correlated noise. Although correlated noise, in particular via matrix factorizations, has been shown to improve accuracy, prior theoretical work focused primarily on the prefix-sum workload. That workload assumes a constant learning rate, whereas in practice learning rate schedules are widely used to accelerate training and improve convergence. We close this gap by deriving general upper and lower bounds for a broad class of learning rate schedules in both single- and multi-epoch settings. Building on these results, we propose a learning-rate-aware factorization that achieves improvements over prefix-sum factorizations under both MaxSE and MeanSE error metrics. Our theoretical analysis yields memory-efficient constructions suitable for practical deployment, and experiments on CIFAR-10 and IMDB datasets confirm that schedule-aware factorizations improve accuracy in private training.