Learning rate scheduling with matrix factorization for private training

conference paper Learning rate scheduling with matrix factorization for private training LIPIcs published yes Nikita Kalinin author 4b14526e-14d2-11ed-ba64-c14c9553d137 Joel D Andersson author 4a893819-d954-11f0-89b1-e360bad9ccc5 ChLa department GradSch department MoHe department FORC: Symposium on Foundations of Responsible Computing The design and evaluation of modern fully dynamic data structures project 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. https://research-explorer.ista.ac.at/download/22146/22149/2026_LIPIcsFORC_Kalinin.pdf application/pdfno Schloss Dagstuhl - Leibniz-Zentrum für Informatik2026Cambridge, MA; United States eng differential privacymachine learningmatrix factorization 7th Symposium on Foundations of Responsible Computing 1868-8969 9783959774192 2511.1799410.4230/LIPIcs.FORC.2026.2 368 N. Kalinin, J.D. Andersson, in:, 7th Symposium on Foundations of Responsible Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. Kalinin, Nikita, and Joel D. Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” 7th Symposium on Foundations of Responsible Computing, vol. 368, 2:1-2:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href="https://doi.org/10.4230/LIPIcs.FORC.2026.2">10.4230/LIPIcs.FORC.2026.2</a>. Kalinin N, Andersson JD. Learning rate scheduling with matrix factorization for private training. In: 7th Symposium on Foundations of Responsible Computing. Vol 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPIcs.FORC.2026.2">10.4230/LIPIcs.FORC.2026.2</a> N. Kalinin and J. D. Andersson, “Learning rate scheduling with matrix factorization for private training,” in 7th Symposium on Foundations of Responsible Computing, Cambridge, MA; United States, 2026, vol. 368. Kalinin, Nikita, and Joel D Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” In 7th Symposium on Foundations of Responsible Computing, Vol. 368. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href="https://doi.org/10.4230/LIPIcs.FORC.2026.2">https://doi.org/10.4230/LIPIcs.FORC.2026.2</a>. Kalinin, N., & Andersson, J. D. (2026). Learning rate scheduling with matrix factorization for private training. In 7th Symposium on Foundations of Responsible Computing (Vol. 368). Cambridge, MA; United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.FORC.2026.2">https://doi.org/10.4230/LIPIcs.FORC.2026.2</a> Kalinin N, Andersson JD. 2026. Learning rate scheduling with matrix factorization for private training. 7th Symposium on Foundations of Responsible Computing. FORC: Symposium on Foundations of Responsible Computing, LIPIcs, vol. 368, 2:1-2:21. 221462026-06-28T22:01:34Z2026-06-29T06:56:34Z