Kernel gradient descent algorithm based on Cauchy loss function

This paper investigates the convergence properties of a kernel gradient descent method for regression with the Cauchy loss in a reproducing kernel Hilbert space (RKHS). It derives near optimal convergence rates by projecting the iterative solution and performing an error decomposition under suitable assumptions. Compared with kernel least squares, Kernel Huber regression, and support vector regression, The experimental results on both simulated and real datasets show that the proposed method exhibits strong robustness under heavy-tailed noise or outliers.