Year: 2026
Type: preprint
Abstract: In this paper, we investigate the generalization performance of distributed gradient descent algorithms in a reproducing kernel Hilbert space under a robust loss function $l_σ$. By exploiting the spectral characterization of gradient descent together with the intrinsic properties of robust loss functions, we establish optimal learning rates for the distributed kernel-based robust gradient descent (DKRGD) algorithm with an appropriately chosen scale parameter $σ$. The proposed parameter choice of $σ$ simultaneously alleviates the saturation phenomenon and guarantees statistical robustness. A key technical contribution is a novel error analysis that provides substantially sharper bounds for products of operators, thereby significantly relaxing existing restrictions on the maximum number of local machines while retaining optimal learning rates. Finally, we develop a communication-efficient strategy that further improves the convergence performance of DKRGD.
Source: arXiv (Cornell University)
Authors: Meng, Jun-Yi, Guo, Zheng-Chu, Mao, Yuan
Institutions: Zhejiang University, Huazhong Agricultural University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212277878