# Lepskii Principle for Distributed Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2409.05070 · HTML: https://mlsanity.com/paper/2409.05070/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 39 references that are in the map.
- First posted on arXiv 8 Sep 2024.

## Builds on (most cited first, 3 of 3)

- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Distributed Kernel Ridge Regression with Communications](https://mlsanity.com/paper/2003.12210/) (2020)
- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)

## Built on by (most cited first, 1 of 1)

- [Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guarantees](https://mlsanity.com/paper/2608.25513/) (2026)

## Abstract (arXiv)

Parameter selection without communicating local data is quite challenging in distributed learning, exhibing an inconsistency between theoretical analysis and practical application of it in tackling distributively stored data. Motivated by the recently developed Lepskii principle and non-privacy communication protocol for kernel learning, we propose a Lepskii principle to equip distributed kernel ridge regression (DKRR) and consequently develop an adaptive DKRR with Lepskii principle (Lep-AdaDKRR for short) by using a double weighted averaging synthesization scheme. We deduce optimal learning rates for Lep-AdaDKRR and theoretically show that Lep-AdaDKRR succeeds in adapting to the regularity of regression functions, effective dimension decaying rate of kernels and different metrics of generalization, which fills the gap of the mentioned inconsistency between theory and application.