Scalable Private Partition Selection via Adaptive Weighting

TL;DR

This paper introduces scalable, adaptive algorithms for private partition selection that improve output utility and scalability in large datasets while maintaining differential privacy, advancing privacy-preserving data analysis methods.

Contribution

The paper presents MAD and MAD2R algorithms that adaptively reweight items for better privacy-utility trade-offs and demonstrate scalability to massive datasets.

Findings

MAD outperforms standard algorithms in parallel settings.

MAD2R maximizes item output through a two-round biasing process.

Algorithms scale to datasets with hundreds of billions of items.

Abstract

In the differentially private partition selection problem (a.k.a. private set union, private key discovery), users hold subsets of items from an unbounded universe. The goal is to output as many items as possible from the union of the users' sets while maintaining user-level differential privacy. Solutions to this problem are a core building block for many privacy-preserving ML applications including vocabulary extraction in a private corpus, computing statistics over categorical data and learning embeddings over user-provided items. We propose an algorithm for this problem, MaxAdaptiveDegree (MAD), which adaptively reroutes weight from items with weight far above the threshold needed for privacy to items with smaller weight, thereby increasing the probability that less frequent items are output. Our algorithm can be efficiently implemented in massively parallel computation systems allowing scalability to very large datasets. We prove that our algorithm stochastically dominates the standard parallel algorithm for this problem. We also develop a two-round version of our algorithm, MAD2R, where results of the computation in the first round are used to bias the weighting in the second round to maximize the number of items output. In experiments, our algorithms provide the best results among parallel algorithms and scale to datasets with hundreds of billions of items, up to three orders of magnitude larger than those analyzed by prior sequential algorithms.