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

In federated frequency estimation (FFE), multiple clients work together to estimate the frequencies of their collective data by communicating with a server that respects the privacy constraints of Secure Summation (SecSum), a cryptographic multi-party computation protocol that ensures that the server can only access the sum of client-held vectors. For single-round FFE, it is known that count sketching is nearly information-theoretically optimal for achieving the fundamental accuracy-communication trade-offs [Chen et al., 2022]. However, we show that under the more practical multi-round FEE setting, simple adaptations of count sketching are strictly sub-optimal, and we propose a novel hybrid sketching algorithm that is provably more accurate. We also address the following fundamental question: how should a practitioner set the sketch size in a way that adapts to the hardness of the underlying problem? We propose a two-phase approach that allows for the use of a smaller sketch size for simpler problems (e.g., near-sparse or light-tailed distributions). We conclude our work by showing how differential privacy can be added to our algorithm and verifying its superior performance through extensive experiments conducted on large-scale datasets.