Analysis of Distributed Stochastic Dual Coordinate Ascent

In 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.