We present two new local differentially private algorithms for frequency estimation. One solves the fundamental frequency oracle problem; the other solves the well-known heavy hitters identification problem. Consistent with prior art, these are randomized algorithms. As a function of failure probability~$\beta$, the former achieves optimal worst-case estimation error for every~$\beta$, while the latter is optimal when~$\beta$ is at least inverse polynomial in~$n$, the number of users. In both algorithms, server running time is~$\tilde{O}(n)$ while user running time is~$\tilde{O}(1)$. Our frequency-oracle algorithm achieves lower estimation error than the prior works of Bassily et al. (NeurIPS 2017). On the other hand, our heavy hitters identification method is as easily implementable as as TreeHist (Bassily et al., 2017) and has superior worst-case error, by a factor of $\Omega(\sqrt{\log n})$.

中文翻译：

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局部差分私有频率估计

我们提出了两种新的用于频率估计的本地差分私有算法。一是解决基频预言机问题；另一个解决了著名的重量级击球手识别问题。与现有技术一致，这些是随机算法。作为失败概率~$\beta$的函数，前者对每个~$\beta$实现最优的最坏情况估计误差，而当~$\beta$至少是~$n$的逆多项式时，后者是最优的，用户数。在这两种算法中，服务器运行时间为~$\tilde{O}(n)$，而用户运行时间为~$\tilde{O}(1)$。我们的频率预言算法比 Bassily 等人的先前工作实现了更低的估计误差。（NeurIPS 2017）。另一方面，我们的重击者识别方法与 TreeHist 一样容易实现（Bassily 等人，