Asymptotically Optimal Locally Private Heavy Hitters via Parameterized Sketches

TL;DR

This paper introduces two new locally private algorithms for frequency estimation and heavy hitters detection, achieving optimal error bounds with efficient computation, improving upon prior methods in accuracy and implementation simplicity.

Contribution

The paper presents novel locally private algorithms for frequency oracle and heavy hitters detection with optimal error bounds and efficient runtime, surpassing previous approaches.

Findings

Frequency oracle algorithm achieves optimal worst-case error for all failure probabilities.

Heavy hitters algorithm has superior worst-case error by a factor of A9( extrm{log} n) compared to TreeHist.

Algorithms run in  ilde{O}(n) server time and  ilde{O}(1) user time.

Abstract

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 $\Omega(\sqrt{\log n})$.