Composition theorems are general and powerful tools that facilitate privacy accounting across multiple data accesses from per-access privacy bounds. However they often result in weaker bounds compared with end-to-end analysis. Two popular tools that mitigate that are the exponential mechanism (or report noisy max) and the sparse vector technique, generalized in a recent private selection framework by Liu and Talwar (STOC 2019). In this work, we propose a flexible framework of private selection and testing that generalizes the one proposed by Liu and Talwar, supporting a wide range of applications. We apply our framework to solve several fundamental tasks, including query releasing, top-k selection, and stable selection, with improved confidence-accuracy tradeoffs. Additionally, for online settings, we apply our private testing to design a mechanism for adaptive query releasing, which improves the sample complexity dependence on the confidence parameter for the celebrated private multiplicative weights algorithm of Hardt and Rothblum (FOCS 2010).
@InProceedings{cohen_et_al:LIPIcs.ITCS.2023.39, author = {Cohen, Edith and Lyu, Xin and Nelson, Jelani and Sarl\'{o}s, Tam\'{a}s and Stemmer, Uri}, title = {{Generalized Private Selection and Testing with High Confidence}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {39:1--39:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.39}, URN = {urn:nbn:de:0030-drops-175426}, doi = {10.4230/LIPIcs.ITCS.2023.39}, annote = {Keywords: differential privacy, sparse vector technique, adaptive data analysis} }
Feedback for Dagstuhl Publishing