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arXiv · 2411.00921

Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization

Giorgio Micali·Clement Lezane·Annika Betken
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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.

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Giorgio Micali, Clement Lezane, Annika Betken. 2024-11-01. Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization. https://arxiv.org/abs/2411.00921

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