Locally Private Sampling with Public Data

Local differential privacy (LDP) is increasingly employed in privacy-preserving machine learning to protect user data before sharing it with an untrusted aggregator. Most LDP methods assume that users possess only a single data record, which is a significant limitation since users often gather extensive datasets (e.g., images, text, time-series data) and frequently have access to public datasets. To address this limitation, we propose a locally private sampling framework that leverages both the private and public datasets of each user. Specifically, we assume each user has two distributions: p and q that represent their private dataset and the public dataset, respectively. The objective is to design a mechanism that generates a private sample approximating p while simultaneously preserving q. We frame this objective as a minimax optimization problem using f-divergence as the utility measure. We fully characterize the minimax optimal mechanisms for general f-divergences provided that p and q are discrete distributions. Remarkably, we demonstrate that this optimal mechanism is universal across all f-divergences. Experiments validate the effectiveness of our minimax optimal sampler compared to the state-of-the-art locally private sampler.