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Life sciences · Preprint
arXiv · September 10, 2026
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This is a preprint presenting a theoretical analysis of distributed kernel-based robust gradient descent algorithms in reproducing kernel Hilbert spaces. The authors derive optimal learning rates and propose a parameter choice strategy; the work is mathematical and does not evaluate clinical, biological, or health outcomes and is not peer reviewed.
Preprint.
Optimal learning rates established for distributed kernel-based robust gradient descent with robust loss function l_σ Proposed parameter choice of σ alleviates saturation phenomenon and guarantees statistical robustness Novel error analysis provides sharper bounds for products of operators
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This is a theoretical machine-learning paper establishing mathematical bounds for a distributed algorithm; it does not report empirical clinical, biological, or health outcomes and does not bear on clinical practice.
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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.
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