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Communication-Efficient Algorithms for Statistical Optimization

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Figure 1: The error ∥�θ−θ∗∥22 versus number of machines, with standard errors across twenty simu-lations, for solving least squares with data generated according to the normal model (16).The oracle least-squares estimate using all N samples is given by the line “All,” while theline “Single” gives the performance of the naive estimator using only n = N/m samples.
Figure 2: Comparison of AVGM and SGDAVGM methods as in Figure 1 plotted on logarithmicscale
Figure 3: The error ∥�θ−θ∗∥22 plotted against the number of machines m for the AVGM and SAVGMmethods, with standard errors across twenty simulations, using the normal regressionmodel (16)
Figure 5: The error ∥�θ−θ∗∥22 plotted against the number of machines m for the AVGM and SAVGMmethods using regression model (17).
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