Optimal Differentially Private Model Training with Public Data

Andrew Lowy, Zeman Li, Tianjian Huang, Meisam Razaviyayn
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:32849-32903, 2024.

Abstract

Differential privacy (DP) ensures that training a machine learning model does not leak private data. In practice, we may have access to auxiliary public data that is free of privacy concerns. In this work, we assume access to a given amount of public data and settle the following fundamental open questions: 1. What is the optimal (worst-case) error of a DP model trained over a private data set while having access to side public data? 2. How can we harness public data to improve DP model training in practice? We consider these questions in both the local and central models of pure and approximate DP. To answer the first question, we prove tight (up to log factors) lower and upper bounds that characterize the optimal error rates of three fundamental problems: mean estimation, empirical risk minimization, and stochastic convex optimization. We show that the optimal error rates can be attained (up to log factors) by either discarding private data and training a public model, or treating public data like it is private and using an optimal DP algorithm. To address the second question, we develop novel algorithms that are "even more optimal" (i.e. better constants) than the asymptotically optimal approaches described above. For local DP mean estimation, our algorithm is optimal including constants. Empirically, our algorithms show benefits over the state-of-the-art.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-lowy24a, title = {Optimal Differentially Private Model Training with Public Data}, author = {Lowy, Andrew and Li, Zeman and Huang, Tianjian and Razaviyayn, Meisam}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {32849--32903}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/lowy24a/lowy24a.pdf}, url = {https://proceedings.mlr.press/v235/lowy24a.html}, abstract = {Differential privacy (DP) ensures that training a machine learning model does not leak private data. In practice, we may have access to auxiliary public data that is free of privacy concerns. In this work, we assume access to a given amount of public data and settle the following fundamental open questions: 1. What is the optimal (worst-case) error of a DP model trained over a private data set while having access to side public data? 2. How can we harness public data to improve DP model training in practice? We consider these questions in both the local and central models of pure and approximate DP. To answer the first question, we prove tight (up to log factors) lower and upper bounds that characterize the optimal error rates of three fundamental problems: mean estimation, empirical risk minimization, and stochastic convex optimization. We show that the optimal error rates can be attained (up to log factors) by either discarding private data and training a public model, or treating public data like it is private and using an optimal DP algorithm. To address the second question, we develop novel algorithms that are "even more optimal" (i.e. better constants) than the asymptotically optimal approaches described above. For local DP mean estimation, our algorithm is optimal including constants. Empirically, our algorithms show benefits over the state-of-the-art.} }
Endnote
%0 Conference Paper %T Optimal Differentially Private Model Training with Public Data %A Andrew Lowy %A Zeman Li %A Tianjian Huang %A Meisam Razaviyayn %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-lowy24a %I PMLR %P 32849--32903 %U https://proceedings.mlr.press/v235/lowy24a.html %V 235 %X Differential privacy (DP) ensures that training a machine learning model does not leak private data. In practice, we may have access to auxiliary public data that is free of privacy concerns. In this work, we assume access to a given amount of public data and settle the following fundamental open questions: 1. What is the optimal (worst-case) error of a DP model trained over a private data set while having access to side public data? 2. How can we harness public data to improve DP model training in practice? We consider these questions in both the local and central models of pure and approximate DP. To answer the first question, we prove tight (up to log factors) lower and upper bounds that characterize the optimal error rates of three fundamental problems: mean estimation, empirical risk minimization, and stochastic convex optimization. We show that the optimal error rates can be attained (up to log factors) by either discarding private data and training a public model, or treating public data like it is private and using an optimal DP algorithm. To address the second question, we develop novel algorithms that are "even more optimal" (i.e. better constants) than the asymptotically optimal approaches described above. For local DP mean estimation, our algorithm is optimal including constants. Empirically, our algorithms show benefits over the state-of-the-art.
APA
Lowy, A., Li, Z., Huang, T. & Razaviyayn, M.. (2024). Optimal Differentially Private Model Training with Public Data. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:32849-32903 Available from https://proceedings.mlr.press/v235/lowy24a.html.

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