Top-k Discovery Under Local Differential Privacy: An Adaptive Sampling Approach

Local differential privacy (LDP) is a promising privacy model for data collection that protects sensitive information of individuals. However, applying LDP to top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> estimation in set-valued data (e.g., identifying most frequent <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> items) may yield poor results for small and sparse datasets due to high sensitivity and heavy perturbation. To address this, we propose an adaptive approach that frames the problem as a multi-armed bandit (MAB) problem, in which the decision-maker selects actions based on information collected from previous rounds to maximize the total reward over time. Inspired by this, we present two adaptive sampling schemes based on MAB: <b>ARBS</b> for identifying top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> items and <b>ARBSF</b> for both top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> item discovery and frequency estimation on these items. Furthermore, to address the potential long delay of multi-round collection, we propose an optimization technique to reduce the time complexity. Both theoretical and empirical results show that our adaptive sampling schemes significantly outperform existing alternatives.