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Generalization Analysis of Distributed Kernel-based Robust Gradient Descent Algorithms

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Updated 4 h ago · first seen 11 Sept 2026

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Published: 11 Sept 2026; T1 · 4 h ago
arXiv: 2609.11712; T1 · 4 h ago
Category: stat.ML; T1 · 4 h ago

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 $l_{\sigma}$. 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 $\sigma$. The proposed parameter choice of $\sigma$ 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.

Authors 3

Jun-Yi Meng, Zheng-Chu Guo, Yuan Mao

Specification

Official page: arxiv.org/abs/2609.11712
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
arXiv id: 2609.11712
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Categories: stat.ML, cs.LG, math.OA, math.PR
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
PDF: arxiv.org/pdf/2609.11712
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Primary category: stat.ML
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh

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T19

Freshest observation

4 h ago

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None

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Claim history · Abstract

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Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
In this paper, we investigate the generalization performance of distributed gradient descent algorithms in a reproducing kernel Hilbert space under a robust loss function $l_{\sigma}$. 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 $\sigma$. The proposed parameter choice of $\sigma$ 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.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	3 h ago	1

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