# Generalization Analysis of Distributed Kernel-based Robust Gradient Descent Algorithms

arXiv: https://arxiv.org/abs/2609.11712 · HTML: https://mlsanity.com/paper/2609.11712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [On Nonconvex Decentralized Gradient Descent](https://mlsanity.com/paper/1608.05766/) (2016)
- [Distributed Kernel Ridge Regression with Communications](https://mlsanity.com/paper/2003.12210/) (2020)
- [A Distributed One-Step Estimator](https://mlsanity.com/paper/1511.01443/) (2015)
- [A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning](https://mlsanity.com/paper/1404.2644/) (2014)
- [Optimality of Robust Online Learning](https://mlsanity.com/paper/2304.10060/) (2023)
- [Distributed Gradient Descent for Functional Learning](https://mlsanity.com/paper/2305.07408/) (2023)
- [Distributed Learning with Discretely Observed Functional Data](https://mlsanity.com/paper/2410.02376/) (2024)

## Abstract (arXiv)

In this paper, we investigate the generalization performance of distributed gradient descent algorithms in a reproducing kernel Hilbert space under a robust loss function lσ. 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.