  In \citep{Yangnips13}, the author presented distributed stochastic dual
coordinate ascent (DisDCA) algorithms for solving large-scale regularized loss
minimization. Extraordinary performances have been observed and reported for
the well-motivated updates, as referred to the practical updates, compared to
the naive updates. However, no serious analysis has been provided to understand
the updates and therefore the convergence rates. In the paper, we bridge the
gap by providing a theoretical analysis of the convergence rates of the
practical DisDCA algorithm. Our analysis helped by empirical studies has shown
that it could yield an exponential speed-up in the convergence by increasing
the number of dual updates at each iteration. This result justifies the
superior performances of the practical DisDCA as compared to the naive variant.
As a byproduct, our analysis also reveals the convergence behavior of the
one-communication DisDCA.
