Private Federated Frequency Estimation: Adapting to the Hardness of the Instance

Jingfeng Wu · Wennan Zhu · Peter Kairouz · Vladimir Braverman

Great Hall & Hall B1+B2 (level 1) #1123
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Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: In federated frequency estimation (FFE), multiple clients work together to estimate the frequency of their local data by communicating with a server, while maintaining the security constraint of $\mathtt{secsum}$ where the server can only access the sum of client-held vectors. For FFE with a single communication round, it is known that count sketch is nearly information-theoretically optimal [Chen et al., 2022]. However, when multiple communication rounds are allowed, we propose a new sketch algorithm that is provably more accurate than a naive adaptation of count sketch. Furthermore, we show that both our sketch algorithm and count sketch can achieve better accuracy when the problem instance is simpler. Therefore, we propose a two-phase approach to enable the use of a smaller sketch size for simpler problems. Finally, we provide mechanisms to make our proposed algorithm differentially private. We verify the performance of our methods through experiments conducted on real datasets.

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