Locally private Gaussian estimation

We study a basic private estimation problem: each of n users draws a single i.i.d. sample from an unknown Gaussian distribution N(µ, s²), and the goal is to estimate µ while guaranteeing local differential privacy for each user. As minimizing the number of rounds of interaction is important in the local setting, we provide adaptive two-round solutions and nonadaptive one-round solutions to this problem. We match these upper bounds with an information-theoretic lower bound showing that our accuracy guarantees are tight up to logarithmic factors for all sequentially interactive locally private protocols.