We study a basic private estimation problem: each of $n$ users draws a single
i.i.d. sample from an unknown Gaussian distribution, and the goal is to
estimate the mean of this Gaussian distribution while satisfying local
differential privacy for each user. Informally, local differential privacy
requires that each data point is individually and independently privatized
before it is passed to a learning algorithm. Locally private Gaussian
estimation is therefore difficult because the data domain is unbounded: users
may draw arbitrarily different inputs, but local differential privacy
nonetheless mandates that different users have (worst-case) similar privatized
output distributions. We provide both adaptive two-round solutions and
nonadaptive one-round solutions for locally private Gaussian estimation. We
then partially match these upper bounds with an information-theoretic lower
bound. This lower bound shows that our accuracy guarantees are tight up to
logarithmic factors for all sequentially interactive
$(\varepsilon,\delta)$-locally private protocols.

研究局部差分隐私在高斯分布参数估计中的应用，并给出了自适应的两轮解决方案和非自适应的一轮解决方案，并通过信息理论下界证明了准确性保证的紧密性。