Randomized Distributed Mean Estimation: Accuracy vs Communication

Jakub Konečný, Peter Richtárik

Research output: Working paper

Abstract / Description of output

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 ${\cal O}\left(1/(\epsilon n)\right)$ 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 $\mathcal{O}(r/n)$ error, where $r$ is the number of bits used to represent a floating point value.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 22 Nov 2016

Keywords / Materials (for Non-textual outputs)

  • cs.DC
  • math.NA
  • stat.ML

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