Improved Communication Efficiency for Distributed Mean Estimation with Side Information

In this paper, we consider the distributed mean estimation problem where the server has access to some side information, e.g., its local computed mean estimation or the received information sent by the distributed clients at the previous iterations. We propose a practical and efficient estimator based on an r-bit Wynzer-Ziv estimator proposed by Mayekar et al., which requires no probabilistic assumption on the data. Unlike Mayekar's work which only utilizes side information at the server, our scheme jointly exploits the correlation between clients' data and server's side information, and also between data of different clients. We derive an upper bound of the estimation error of the proposed estimator. Based on this upper bound, we provide two algorithms on how to choose input parameters for the estimator. Finally, parameter regions in which our estimator is better than the previous one are characterized.