Differentially private algorithms for linear queries via stochastic convex optimization

Giorgio Micali, Clement LEZANE, Annika Betken
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1414-1422, 2025.

Abstract

This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms’ accuracy with reference to the true data-generating distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-micali25a, title = {Differentially private algorithms for linear queries via stochastic convex optimization}, author = {Micali, Giorgio and LEZANE, Clement and Betken, Annika}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {1414--1422}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/micali25a/micali25a.pdf}, url = {https://proceedings.mlr.press/v258/micali25a.html}, abstract = {This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms’ accuracy with reference to the true data-generating distribution.} }
Endnote
%0 Conference Paper %T Differentially private algorithms for linear queries via stochastic convex optimization %A Giorgio Micali %A Clement LEZANE %A Annika Betken %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-micali25a %I PMLR %P 1414--1422 %U https://proceedings.mlr.press/v258/micali25a.html %V 258 %X This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem whose solution corresponds to a distribution minimizing the difference between answers to the linear queries based on the true distribution and answers from a differentially private distribution. Against this background, we establish two new algorithms for corresponding differentially private data release: the first is based on the differentially private Frank-Wolfe method, the second combines randomized smoothing with stochastic convex optimization techniques for a solution to the saddle-point problem. While previous works assess the accuracy of differentially private algorithms with reference to the empirical data distribution, a key contribution of our work is a more natural evaluation of the proposed algorithms’ accuracy with reference to the true data-generating distribution.
APA
Micali, G., LEZANE, C. & Betken, A.. (2025). Differentially private algorithms for linear queries via stochastic convex optimization. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1414-1422 Available from https://proceedings.mlr.press/v258/micali25a.html.

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