Distributed learning with partial coefficients regularization

Abstract

We study distributed learning with partial coefficients regularization scheme in a reproducing kernel Hilbert space (RKHS). The algorithm randomly partitions the sample set [Formula: see text] into [Formula: see text] disjoint sample subsets of equal size. In order to reduce the complexity of algorithms, we apply a partial coefficients regularization scheme to each sample subset to produce an output function, and average the individual output functions to get the final global estimator. The error bound in the [Formula: see text]-metric is deduced and the asymptotic convergence for this distributed learning with partial coefficients regularization is proved by the integral operator technique. Satisfactory learning rates are then derived under a standard regularity condition on the regression function, which reveals an interesting phenomenon that when [Formula: see text] and [Formula: see text] is small enough, this distributed learning has the same convergence rate with the algorithm processing the whole data in one single machine.