Practical Locally Private Heavy Hitters

TL;DR

This paper introduces practical local differentially private algorithms, TreeHist and Bitstogram, that significantly improve efficiency and are suitable for large-scale real-world applications, with implementations validated against Google's RAPPOR.

Contribution

The paper presents two new algorithms, TreeHist and Bitstogram, achieving near-optimal error with substantially reduced running times, especially at the user level, compared to previous methods.

Findings

Algorithms achieve optimal or near-optimal error bounds.

Server running time is approximately linear in the number of users.

User running time is nearly constant, enabling large-scale deployment.

Abstract

We present new practical local differentially private heavy hitters algorithms achieving optimal or near-optimal worst-case error and running time -- TreeHist and Bitstogram. In both algorithms, server running time is $\tilde O(n)$ and user running time is $\tilde O(1)$, hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring $O(n^{5/2})$ server time and $O(n^{3/2})$ user time. With a typically large number of participants in local algorithms ($n$ in the millions), this reduction in time complexity, in particular at the user side, is crucial for making locally private heavy hitters algorithms usable in practice. We implemented Algorithm TreeHist to verify our theoretical analysis and compared its performance with the performance of Google's RAPPOR code.