Distributed Semi-supervised Regression Learning with Coefficient Regularization

We consider the generalization ability of distributed learning with coefficient-based regularization equipped with a divide-and-conquer approach and semi-supervised algorithm in a reproducing kernel Hilbert space. The algorithm applies semi-supervised coefficient regularization regression to m disjoint sample subsets of equal size that are distributively stored on multiple servers to produce the individual output functions, and then averages the individual output functions to get the final global estimator. Using a second order decomposition on difference of operator inverses approach and a novel error decomposition, we derive optimal learning rates for the algorithm in expectation and also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning.