On Avoiding the Union Bound When Answering Multiple Differentially Private Queries

• URL: http://arxiv.org/abs/2012.09116v1
• Date: Wed, 16 Dec 2020 17:58:45 GMT
• Title: On Avoiding the Union Bound When Answering Multiple Differentially Private Queries
• Authors: Badih Ghazi, Ravi Kumar, Pasin Manurangsi
• Abstract summary: We give an algorithm for this task that achieves an expected $ell_infty$ error bound of $O(frac1epsilonsqrtk log frac1delta)$. On the other hand, the algorithm of Dagan and Kur has a remarkable advantage that the $ell_infty$ error bound of $O(frac1epsilonsqrtk log frac1delta)$ holds not only in expectation but always.
• Score: 49.453751858361265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we study the problem of answering $k$ queries with $(\epsilon, \delta)$-differential privacy, where each query has sensitivity one. We give an algorithm for this task that achieves an expected $\ell_\infty$ error bound of $O(\frac{1}{\epsilon}\sqrt{k \log \frac{1}{\delta}})$, which is known to be tight (Steinke and Ullman, 2016). A very recent work by Dagan and Kur (2020) provides a similar result, albeit via a completely different approach. One difference between our work and theirs is that our guarantee holds even when $\delta < 2^{-\Omega(k/(\log k)^8)}$ whereas theirs does not apply in this case. On the other hand, the algorithm of Dagan and Kur has a remarkable advantage that the $\ell_{\infty}$ error bound of $O(\frac{1}{\epsilon}\sqrt{k \log \frac{1}{\delta}})$ holds not only in expectation but always (i.e., with probability one) while we can only get a high probability (or expected) guarantee on the error.

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