文章基本信息

标题：The Complexity of Computing the Optimal Composition of Differential Privacy
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作者：Jack Murtagh ; Salil Vadhan
期刊名称：Theory of Computing
印刷版ISSN：1557-2862
电子版ISSN：1557-2862
出版年度：2018
卷号：14
页码：1-35
DOI：10.4086/toc.2018.v014a008
出版社：University of Chicago
摘要：In the study of differential privacy, composition theorems (starting with the original paper of Dwork, McSherry, Nissim, and Smith (TCC’06)) bound the degradation of privacy when composing several differentially private algorithms. Kairouz, Oh, and Viswanath (ICML’15) showed how to compute the optimal bound for composing k arbitrary (ε,δ)-differentially private algorithms. We characterize the optimal composition for the more general case of k arbitrary (ε1,δ1),...,(εk,δk)-differentially private algorithms where the privacy parameters may differ for each algorithm in the composition. We show that computing the optimal composition in general is #P-complete. Since computing optimal composition exactly is infeasible (unless FP = #P), we give an approximation algorithm that computes the composition to arbitrary accuracy in polynomial time. The algorithm is a modification of Dyer’s dynamic programming approach to approximately counting solutions to knapsack problems (STOC’03).
关键词：complexity theory; approximation algorithms; differential privacy; composition