# Distributed Kernel Ridge Regression with Communications

arXiv: https://arxiv.org/abs/2003.12210 · HTML: https://mlsanity.com/paper/2003.12210/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 14 of 14)

- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Optimal Kernel Quantile Learning with Random Features](https://mlsanity.com/paper/2408.13591/) (2024)
- [Nystr"om Regularization for Time Series Forecasting](https://mlsanity.com/paper/2111.07109/) (2021)
- [Transfer Learning for Kernel-based Regression](https://mlsanity.com/paper/2310.13966/) (2023)
- [Adaptive Parameter Selection for Kernel Ridge Regression](https://mlsanity.com/paper/2312.05885/) (2023)
- [Distributed Semi-Supervised Sparse Statistical Inference](https://mlsanity.com/paper/2306.10395/) (2023)
- [Decentralized Kernel Ridge Regression Based on Data-Dependent Random Feature](https://mlsanity.com/paper/2405.07791/) (2024)
- [Lepskii Principle for Distributed Kernel Ridge Regression](https://mlsanity.com/paper/2409.05070/) (2024)
- [A Kernel Perspective on Distillation-based Collaborative Learning](https://mlsanity.com/paper/2410.17592/) (2024)
- [Kernel-Based Distributed Q-Learning: A Scalable Reinforcement Learning Approach for Dynamic Treatment Regimes](https://mlsanity.com/paper/2302.10434/) (2023)
- [Lp- and Risk Consistency of Localized SVMs](https://mlsanity.com/paper/2305.09385/) (2023)
- [Kernel-Based Learning of Chest X-ray Images for Predicting ICU Escalation among COVID-19 Patients](https://mlsanity.com/paper/2602.10261/) (2026)
- [Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guarantees](https://mlsanity.com/paper/2608.25513/) (2026)
- [Generalization Analysis of Distributed Kernel-based Robust Gradient Descent Algorithms](https://mlsanity.com/paper/2609.11712/) (2026)

## Abstract (arXiv)

This paper focuses on generalization performance analysis for distributed algorithms in the framework of learning theory. Taking distributed kernel ridge regression (DKRR) for example, we succeed in deriving its optimal learning rates in expectation and providing theoretically optimal ranges of the number of local processors. Due to the gap between theory and experiments, we also deduce optimal learning rates for DKRR in probability to essentially reflect the generalization performance and limitations of DKRR. Furthermore, we propose a communication strategy to improve the learning performance of DKRR and demonstrate the power of communications in DKRR via both theoretical assessments and numerical experiments.