Convergence analysis of distributed multi-penalty regularized pairwise learning

In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with L2-error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization.