@inproceedings{22146,
  abstract     = {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.},
  author       = {Kalinin, Nikita and Andersson, Joel D},
  booktitle    = {7th Symposium on Foundations of Responsible Computing},
  isbn         = {9783959774192},
  issn         = {1868-8969},
  keywords     = {differential privacy, machine learning, matrix factorization},
  location     = {Cambridge, MA; United States},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Learning rate scheduling with matrix factorization for private training}},
  doi          = {10.4230/LIPIcs.FORC.2026.2},
  volume       = {368},
  year         = {2026},
}

@inproceedings{20298,
  abstract     = {In this paper, we study the problem of estimating the unknown mean θ of a unit variance Gaussian distribution in a locally differentially private (LDP) way. In the high-privacy regime (ϵ≤1
), we identify an optimal privacy mechanism that minimizes the variance of the estimator asymptotically. Our main technical contribution is the maximization of the Fisher-Information of the sanitized data with respect to the local privacy mechanism Q. We find that the exact solution Qθ,ϵ of this maximization is the sign mechanism that applies randomized response to the sign of Xi−θ, where X1,…,Xn are the confidential iid original samples. However, since this optimal local mechanism depends on the unknown mean θ, we employ a two-stage LDP parameter estimation procedure which requires splitting agents into two groups. The first n1 observations are used to consistently but not necessarily efficiently estimate the parameter θ by θn1~
. Then this estimate is updated by applying the sign mechanism with θ~n1 instead of θ
 to the remaining n−n1 observations, to obtain an LDP and efficient estimator of the unknown mean.},
  author       = {Kalinin, Nikita and Steinberger, Lukas},
  booktitle    = {Proceedings of the 28th International Conference on Artificial Intelligence and Statistics},
  issn         = {2640-3498},
  location     = {Mai Khao, Thailand},
  pages        = {118--126},
  publisher    = {ML Research Press},
  title        = {{Efficient estimation of a Gaussian mean with local differential privacy}},
  volume       = {258},
  year         = {2025},
}

@inproceedings{18875,
  abstract     = {Current state-of-the-art methods for differentially private model training are based on matrix factorization techniques. However, these methods suffer from high computational overhead because they require numerically solving a demanding optimization problem to determine an approximately optimal factorization prior to the actual model training. In this work, we present a new matrix factorization approach, BSR, which overcomes this computational bottleneck. By exploiting properties of the standard matrix square root, BSR allows to efficiently handle also large-scale problems. For the key scenario of stochastic gradient descent with momentum and weight decay, we even derive analytical expressions for BSR that render the computational overhead negligible. We prove bounds on the approximation quality that hold both in the centralized and in the federated learning setting. Our numerical experiments demonstrate that models trained using BSR perform on par with the best existing methods, while completely avoiding their computational overhead.},
  author       = {Kalinin, Nikita and Lampert, Christoph},
  booktitle    = {38th Annual Conference on Neural Information Processing Systems},
  issn         = {1049-5258},
  location     = {Vancouver, Canada},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Banded square root matrix factorization for differentially private model training}},
  volume       = {37},
  year         = {2024},
}