论文标题
在回答多个差异私人查询时避免工会绑定时
On Avoiding the Union Bound When Answering Multiple Differentially Private Queries
论文作者
论文摘要
在这项工作中，我们研究了用$（ε，δ）$ - 差异隐私回答$ k $ Queries的问题，每个查询都具有敏感性。我们为此任务提供了一种算法，该算法实现了$ O（\ frac {1}ε\ sqrt {k \ log \ frac {1}Δ}）$的预期$ \ ell_ \ infty $误差绑定，已知很紧张（Steinke and Ullman，2016）。 Dagan和Kur（2020）最近的一项工作提供了类似的结果，尽管通过完全不同的方法。我们的工作和他们的工作之间的一个区别是，即使$Δ<2^{ - ω（k/（\ log k）^8）} $即使在这种情况下不适用。另一方面，达根（Dagan）和库尔（Kur）的算法具有显着的优势：$ \ ell _ {\ infty} $错误的限制为$ o（\ frac {1} {1}ε\ sqrt {k \ log \ log \ log \ frac {1}δ}δ}Δ} $不仅可以肯定，但始终可以（始终可以）（everence a Probitie a Probity a Probitie a Probity a Probity a Probity a Probity a Probity a Probity a light（ey.e.e.e.e.e.e.e.e），或者是一定的（或者），或者是一定的（或者）。错误。
In this work, we study the problem of answering $k$ queries with $(ε, δ)$-differential privacy, where each query has sensitivity one. We give an algorithm for this task that achieves an expected $\ell_\infty$ error bound of $O(\frac{1}ε\sqrt{k \log \frac{1}δ})$, 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 $δ< 2^{-Ω(k/(\log k)^8)}$ 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 $O(\frac{1}ε\sqrt{k \log \frac{1}δ})$ 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.
