Generalization Analysis of Distributed Kernel-based Robust Gradient Descent

This paper establishes optimal learning rates for distributed kernel-based robust gradient descent (DKRGD) within a reproducing kernel Hilbert space under a robust loss function $l_\sigma$. By refining operator product error bounds, the authors significantly loosen theoretical constraints on the allowable number of distributed machines without sacrificing statistical optimality. The work also offers an analytical criterion for the scale parameter $\sigma$ to mitigate saturation while preserving robustness, accompanied by a communication-efficient execution strategy.