Lower Bounds for Locally Private Estimation via Communication Complexity
In collaboration with Stanford University
authors John Duchi, Ryan Rogers
We develop lower bounds for estimation under local privacy constraints—including differential privacy and its relaxations to approximate or Rényi differential privacy—by showing an equivalence between private estimation and communication-restricted estimation problems. Our results apply to arbitrarily interactive privacy mechanisms, and they also give sharp lower bounds for all levels of differential privacy protections, that is, privacy mechanisms with privacy levels . As a particular consequence of our results, we show that the minimax mean-squared error for estimating the mean of a bounded or Gaussian random vector in dimensions scales as
Understanding how people use their devices often helps in improving the user experience. However, accessing the data that provides such insights — for example, what users type on their keyboards and the websites they visit — can compromise user privacy. We develop a system architecture that enables learning at scale by leveraging local differential privacy, combined with existing privacy best practices. We design efficient and scalable local differentially private algorithms and provide rigorous analyses to demonstrate the tradeoffs among utility, privacy, server computation, and device bandwidth. Understanding the balance among these factors leads us to a successful practical deployment using local differential privacy. This deployment scales to hundreds of millions of users across a variety of use cases, such as identifying popular emojis, popular health data types, and media playback preferences in Safari. We provide additional details about our system in the full version.