Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917826998042624 |
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| author | Micali, Giorgio Lezane, Clement Betken, Annika |
| author_facet | Micali, Giorgio Lezane, Clement Betken, Annika |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization Micali, Giorgio Lezane, Clement Betken, Annika Methodology 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. |
| title | Differentially Private Algorithms for Linear Queries via Stochastic Convex Optimization |
| topic | Methodology |
| url | https://arxiv.org/abs/2411.00921 |