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Front. Appl. Math. Stat. | doi: 10.3389/fams.2018.00062

Randomized Distributed Mean Estimation: Accuracy vs Communication

  • 1University of Edinburgh, United Kingdom
  • 2Google (United States), United States
  • 3Moscow Institute of Physics and Technology, Russia

We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any statistical assumptions about the source of the vectors. This problem arises as a subproblem in many applications, including reduce-all operations within algorithms for distributed and federated optimization and learning. We propose a flexible family of randomized algorithms exploring the trade-off between expected communication cost and estimation error. Our family contains the full-communication and zero-error method on one extreme, and an epsilon-bit communication and O(1/(epsilon n)) error method on the opposite extreme. In the special case where we communicate, in expectation, a single bit per coordinate of each vector, we improve upon existing results by obtaining O(r/n) error, where r is the number of bits used to represent a floating point value.

Keywords: Communication efficiency, Distributed mean estimation, Accuracy-communication tradeoff, Gradient compression, quantization

Received: 11 Oct 2018; Accepted: 28 Nov 2018.

Edited by:

Yiming Ying, University at Albany, United States

Reviewed by:

Shao-Bo Lin, Wenzhou University, China
Shiyin Qin, Beihang University, China  

Copyright: © 2018 Konečný and Richtárik. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: PhD. Jakub Konečný, University of Edinburgh, Edinburgh, United Kingdom, kubo.konecny@gmail.com