Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms

The data for many machine learning tasks are owned by individuals who are typically concerned about privacy. Here, the authors study the optimal design of a data acquisition mechanism aimed at learning the mean of a population. This data acquisition scheme includes the design of a payment rule to compensate users for their privacy loss. It also involves selecting an estimator that minimizes estimation error while simultaneously providing privacy guarantees to users in line with their privacy preferences. The authors formulate this problem as a Bayesian mechanism design problem and propose approximately optimal data acquisition mechanisms.