Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization
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
@article{arxiv.2411.00921,
title = {Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization},
author = {Giorgio Micali and Clement Lezane and Annika Betken},
journal= {arXiv preprint arXiv:2411.00921},
year = {2024}
}