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Communication-Efficient Algorithms for Statistical Optimization
Yuchen Zhang · John Duchi · Martin J Wainwright

Wed Dec 05 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor
We study two communication-efficient algorithms for distributed statistical optimization on large-scale data. The first algorithm is an averaging method that distributes the $N$ data samples evenly to $m$ machines, performs separate minimization on each subset, and then averages the estimates. We provide a sharp analysis of this average mixture algorithm, showing that under a reasonable set of conditions, the combined parameter achieves mean-squared error that decays as $\order(N^{-1}+(N/m)^{-2})$. Whenever $m \le \sqrt{N}$, this guarantee matches the best possible rate achievable by a centralized algorithm having access to all $N$ samples. The second algorithm is a novel method, based on an appropriate form of the bootstrap. Requiring only a single round of communication, it has mean-squared error that decays as $\order(N^{-1}+(N/m)^{-3})$, and so is more robust to the amount of parallelization. We complement our theoretical results with experiments on large-scale problems from the Microsoft Learning to Rank dataset.

Author Information

Yuchen Zhang (UC Berkeley)
John Duchi (Stanford)
Martin J Wainwright (UC Berkeley)

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