Communication-efficient algorithms for statistical optimization

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 O(N^-1 + (N/m)^-2). Whenever m ≤ √N, this guarantee matches the best possible rate achievable by a centralized algorithm with access to all N samples. The second algorithm is a novel method, based on an appropriate form of bootstrap. Requiring only a single round of communication, it has mean-squared error that decays as O(N^-1 + (N/m)^-3), and so is more robust to the amount of parallelization.