[{"volume":368,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","supplementarymaterial":"no","date_created":"2026-06-28T22:01:34Z","status":"public","OA_type":"gold","arxiv":1,"conference":{"end_date":"2026-06-05","name":"FORC: Symposium on Foundations of Responsible Computing","start_date":"2026-06-03","location":"Cambridge, MA; United States"},"scopus_import":"1","ddc":["000"],"day":"01","article_number":"2:1-2:21","language":[{"iso":"eng"}],"citation":{"ista":"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.","short":"N. Kalinin, J.D. Andersson, in:, 7th Symposium on Foundations of Responsible Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","chicago":"Kalinin, Nikita, and Joel D Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” In <i>7th Symposium on Foundations of Responsible Computing</i>, 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>.","ieee":"N. Kalinin and J. D. Andersson, “Learning rate scheduling with matrix factorization for private training,” in <i>7th Symposium on Foundations of Responsible Computing</i>, Cambridge, MA; United States, 2026, vol. 368.","ama":"Kalinin N, Andersson JD. Learning rate scheduling with matrix factorization for private training. In: <i>7th Symposium on Foundations of Responsible Computing</i>. 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>","mla":"Kalinin, Nikita, and Joel D. Andersson. “Learning Rate Scheduling with Matrix Factorization for Private Training.” <i>7th Symposium on Foundations of Responsible Computing</i>, 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>.","apa":"Kalinin, N., &#38; Andersson, J. D. (2026). Learning rate scheduling with matrix factorization for private training. In <i>7th Symposium on Foundations of Responsible Computing</i> (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>"},"department":[{"_id":"ChLa"},{"_id":"GradSch"},{"_id":"MoHe"}],"ec_funded":1,"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures"}],"file":[{"success":1,"access_level":"open_access","creator":"dernst","content_type":"application/pdf","date_updated":"2026-06-29T06:55:23Z","checksum":"c661f016d3861a1c1b590b87a744d087","relation":"main_file","date_created":"2026-06-29T06:55:23Z","file_id":"22149","file_size":1231914,"file_name":"2026_LIPIcsFORC_Kalinin.pdf"}],"OA_place":"publisher","researchdata_availability":"no","corr_author":"1","title":"Learning rate scheduling with matrix factorization for private training","date_updated":"2026-06-29T06:56:34Z","doi":"10.4230/LIPIcs.FORC.2026.2","publication":"7th Symposium on Foundations of Responsible Computing","alternative_title":["LIPIcs"],"file_date_updated":"2026-06-29T06:55:23Z","das_tickbox":"0","external_id":{"arxiv":["2511.17994"]},"intvolume":"       368","quality_controlled":"1","type":"conference","publication_status":"published","month":"06","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-06-01T00:00:00Z","_id":"22146","has_accepted_license":"1","publication_identifier":{"isbn":["9783959774192"],"eissn":["1868-8969"]},"article_processing_charge":"No","abstract":[{"lang":"eng","text":"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":[{"full_name":"Kalinin, Nikita","last_name":"Kalinin","first_name":"Nikita","id":"4b14526e-14d2-11ed-ba64-c14c9553d137"},{"id":"4a893819-d954-11f0-89b1-e360bad9ccc5","first_name":"Joel D","last_name":"Andersson","full_name":"Andersson, Joel D"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"oa":1,"year":"2026","acknowledgement":"We thank Rasmus Pagh, Christoph Lampert and Jalaj Upadhyay for valuable\r\ncomments on an early draft. We thank Ryan Mckenna for a fruitful discussion on the experiment\r\ndesign. We thank Antti Honkela for sharing insights on learning rate scheduling and DP.\r\nNikita P. Kalinin: Funded in part by the Austrian Science Fund (FWF) [10.55776/COE12].\r\nJoel Daniel Andersson: Funded by the European Union. Views and opinions expressed are however\r\nthose of the author(s) only and do not necessarily reflect those of the European Union or the European\r\nResearch Council Executive Agency. Neither the European Union nor the granting authority can be\r\nheld responsible for them. This project has received funding from the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (MoDynStruct,\r\nNo. 101019564). Additional funding by Providentia, a Data Science Distinguished Investigator grant\r\nfrom Novo Nordisk Fonden, with additional support from VILLUM Investigator grant 54451.\r\n","keyword":["differential privacy","machine learning","matrix factorization"]},{"date_published":"2025-05-01T00:00:00Z","_id":"20298","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","month":"05","oa_version":"Published Version","quality_controlled":"1","type":"conference","oa":1,"year":"2025","acknowledgement":"We would like to express our gratitude to Christoph Lampert for his valuable insights and fruitful discussions that significantly contributed to the development of this paper.\r\nWe also thank Salil Vadhan for his constructive feedback on an earlier version of this draft.\r\nThe second author gratefully acknowledges support by the Austrian Science Fund (FWF): I 5484-N, as part of the Research Unit 5381 of the German Research Foundation.","abstract":[{"text":"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\r\n), 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~\r\n. Then this estimate is updated by applying the sign mechanism with θ~n1 instead of θ\r\n to the remaining n−n1 observations, to obtain an LDP and efficient estimator of the unknown mean.","lang":"eng"}],"author":[{"full_name":"Kalinin, Nikita","id":"4b14526e-14d2-11ed-ba64-c14c9553d137","last_name":"Kalinin","first_name":"Nikita"},{"last_name":"Steinberger","first_name":"Lukas","full_name":"Steinberger, Lukas"}],"page":"118-126","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","publication_identifier":{"eissn":["2640-3498"]},"ddc":["000"],"day":"01","language":[{"iso":"eng"}],"conference":{"name":"AISTATS: Conference on Artificial Intelligence and Statistics","end_date":"2025-05-05","start_date":"2025-05-03","location":"Mai Khao, Thailand"},"scopus_import":"1","date_created":"2025-09-07T22:01:34Z","status":"public","OA_type":"diamond","arxiv":1,"volume":258,"publisher":"ML Research Press","alternative_title":["PMLR"],"publication":"Proceedings of the 28th International Conference on Artificial Intelligence and Statistics","file_date_updated":"2025-09-09T08:26:44Z","external_id":{"arxiv":["2402.04840"]},"intvolume":"       258","title":"Efficient estimation of a Gaussian mean with local differential privacy","date_updated":"2025-09-09T08:28:41Z","OA_place":"publisher","file":[{"date_created":"2025-09-09T08:26:44Z","relation":"main_file","checksum":"3dcd59988ca974b98662ba09a516e616","file_name":"2025_AISTATS_Kalinin.pdf","file_size":395864,"file_id":"20316","content_type":"application/pdf","access_level":"open_access","creator":"dernst","success":1,"date_updated":"2025-09-09T08:26:44Z"}],"corr_author":"1","citation":{"apa":"Kalinin, N., &#38; Steinberger, L. (2025). Efficient estimation of a Gaussian mean with local differential privacy. In <i>Proceedings of the 28th International Conference on Artificial Intelligence and Statistics</i> (Vol. 258, pp. 118–126). Mai Khao, Thailand: ML Research Press.","mla":"Kalinin, Nikita, and Lukas Steinberger. “Efficient Estimation of a Gaussian Mean with Local Differential Privacy.” <i>Proceedings of the 28th International Conference on Artificial Intelligence and Statistics</i>, vol. 258, ML Research Press, 2025, pp. 118–26.","ama":"Kalinin N, Steinberger L. Efficient estimation of a Gaussian mean with local differential privacy. In: <i>Proceedings of the 28th International Conference on Artificial Intelligence and Statistics</i>. Vol 258. ML Research Press; 2025:118-126.","ieee":"N. Kalinin and L. Steinberger, “Efficient estimation of a Gaussian mean with local differential privacy,” in <i>Proceedings of the 28th International Conference on Artificial Intelligence and Statistics</i>, Mai Khao, Thailand, 2025, vol. 258, pp. 118–126.","chicago":"Kalinin, Nikita, and Lukas Steinberger. “Efficient Estimation of a Gaussian Mean with Local Differential Privacy.” In <i>Proceedings of the 28th International Conference on Artificial Intelligence and Statistics</i>, 258:118–26. ML Research Press, 2025.","short":"N. Kalinin, L. Steinberger, in:, Proceedings of the 28th International Conference on Artificial Intelligence and Statistics, ML Research Press, 2025, pp. 118–126.","ista":"Kalinin N, Steinberger L. 2025. Efficient estimation of a Gaussian mean with local differential privacy. Proceedings of the 28th International Conference on Artificial Intelligence and Statistics. AISTATS: Conference on Artificial Intelligence and Statistics, PMLR, vol. 258, 118–126."},"department":[{"_id":"ChLa"}]},{"author":[{"id":"4b14526e-14d2-11ed-ba64-c14c9553d137","last_name":"Kalinin","first_name":"Nikita","full_name":"Kalinin, Nikita"},{"orcid":"0000-0001-8622-7887","full_name":"Lampert, Christoph","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","first_name":"Christoph","last_name":"Lampert"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"text":"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.","lang":"eng"}],"year":"2024","oa":1,"publication_identifier":{"eissn":["1049-5258"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-12-01T00:00:00Z","_id":"18875","has_accepted_license":"1","type":"conference","quality_controlled":"1","publication_status":"published","month":"12","oa_version":"Published Version","date_updated":"2025-05-14T11:34:20Z","title":"Banded square root matrix factorization for differentially private model training","external_id":{"arxiv":["2405.13763"]},"intvolume":"        37","alternative_title":["Advances in Neural Information Processing Systems"],"publication":"38th Annual Conference on Neural Information Processing Systems","file_date_updated":"2025-01-27T09:52:15Z","department":[{"_id":"GradSch"},{"_id":"ChLa"}],"citation":{"ista":"Kalinin N, Lampert C. 2024. Banded square root matrix factorization for differentially private model training. 38th Annual Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 37.","chicago":"Kalinin, Nikita, and Christoph Lampert. “Banded Square Root Matrix Factorization for Differentially Private Model Training.” In <i>38th Annual Conference on Neural Information Processing Systems</i>, Vol. 37. Neural Information Processing Systems Foundation, 2024.","short":"N. Kalinin, C. Lampert, in:, 38th Annual Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2024.","ieee":"N. Kalinin and C. Lampert, “Banded square root matrix factorization for differentially private model training,” in <i>38th Annual Conference on Neural Information Processing Systems</i>, Vancouver, Canada, 2024, vol. 37.","ama":"Kalinin N, Lampert C. Banded square root matrix factorization for differentially private model training. In: <i>38th Annual Conference on Neural Information Processing Systems</i>. Vol 37. Neural Information Processing Systems Foundation; 2024.","mla":"Kalinin, Nikita, and Christoph Lampert. “Banded Square Root Matrix Factorization for Differentially Private Model Training.” <i>38th Annual Conference on Neural Information Processing Systems</i>, vol. 37, Neural Information Processing Systems Foundation, 2024.","apa":"Kalinin, N., &#38; Lampert, C. (2024). Banded square root matrix factorization for differentially private model training. In <i>38th Annual Conference on Neural Information Processing Systems</i> (Vol. 37). Vancouver, Canada: Neural Information Processing Systems Foundation."},"corr_author":"1","file":[{"checksum":"a216cab8eddc1fe7840aede0e2c0d41e","date_created":"2025-01-27T09:52:15Z","relation":"main_file","file_name":"2024_NeurIPS_Nikita.pdf","file_size":1144656,"file_id":"18888","content_type":"application/pdf","success":1,"creator":"dernst","access_level":"open_access","date_updated":"2025-01-27T09:52:15Z"}],"OA_place":"publisher","scopus_import":"1","conference":{"end_date":"2024-12-16","name":"NeurIPS: Neural Information Processing Systems","start_date":"2024-12-16","location":"Vancouver, Canada"},"ddc":["000"],"language":[{"iso":"eng"}],"day":"01","publisher":"Neural Information Processing Systems Foundation","volume":37,"status":"public","OA_type":"gold","arxiv":1,"date_created":"2025-01-24T17:58:16Z"}]