Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms

Distributed estimation of a Gaussian mean under communication constraints is studied in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between communication costs and statistical accuracy, are established under the independent protocols. Communication-efficient and statistically optimal procedures are developed. In the univariate case, the optimal rate depends only on the total communication budget, so long as each local machine has at least one bit. However, in the multivariate case, the minimax rate depends on the specific …

accuracy algorithms case communication constraints convergence costs decision distributed framework independent mean minimax statistical