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Distributed Mean Estimation with Limited Communication
Ananda Theertha Suresh · Felix Xinnan Yu · Sanjiv Kumar · Brendan McMahan

Mon Aug 07 10:30 PM -- 10:48 PM (PDT) @ C4.8
Motivated by the need for distributed learning and optimization algorithms with low communication cost, we study communication efficient algorithms for distributed mean estimation. Unlike previous works, we make no probabilistic assumptions on the data. We first show that for $d$ dimensional data with $n$ clients, a naive stochastic rounding approach yields a mean squared error (MSE) of $\Theta(d/n)$ and uses a constant number of bits per dimension per client. We then extend this naive algorithm in two ways: we show that applying a structured random rotation before quantization reduces the error to $\mathcal{O}((\log d)/n)$ and a better coding strategy further reduces the error to $\mathcal{O}(1/n)$. We also show that the latter coding strategy is optimal up to a constant in the minimax sense i.e., it achieves the best MSE for a given communication cost. We finally demonstrate the practicality of our algorithms by applying them to distributed Lloyd's algorithm for k-means and power iteration for PCA.

Author Information

Ananda Theertha Suresh (Google Research)
Felix Xinnan Yu (Google Research)
Sanjiv Kumar (Google Research, NY)
Brendan McMahan (Google)

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