Distributed gradient descent algorithm for robust kernel-based regression

In this paper, we study the theoretical underpinning of a gradient descent algorithm with a robust loss function in a reproducing kernel Hilbert space (RKHS) framework. We introduce a novel auxiliary sequence for the error analysis and improve the previous convergence results when the regression function does not lie in the RKHS. Under the universal assumptions, we establish the optimal rates of convergence for distributed robust gradient descent algorithm in both cases where the regression function is inside and outside the RKHS, provided the number of partition is not too large.