# Online Distributed Learning Over Networks in RKH Spaces Using Random Fourier Features

arXiv: https://arxiv.org/abs/1703.08131 · HTML: https://mlsanity.com/paper/1703.08131/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2017.

## Built on by (most cited first, 11 of 11)

- [Online Multi-Agent Forecasting with Interpretable Collaborative Graph Neural Network](https://mlsanity.com/paper/2107.00894/) (2021)
- [Personalized Online Federated Learning with Multiple Kernels](https://mlsanity.com/paper/2311.05108/) (2023)
- [Distributed Online Learning with Multiple Kernels](https://mlsanity.com/paper/2102.12733/) (2021)
- [On the Necessity of Collaboration for Online Model Selection with Decentralized Data](https://mlsanity.com/paper/2404.09494/) (2024)
- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [Graph-Aided Online Multi-Kernel Learning](https://mlsanity.com/paper/2102.04690/) (2021)
- [Random Fourier Feature Based Deep Learning for Wireless Communications](https://mlsanity.com/paper/2101.05254/) (2021)
- [Decentralized Kernel Ridge Regression Based on Data-Dependent Random Feature](https://mlsanity.com/paper/2405.07791/) (2024)
- [Decentralized Online Ensembles of Gaussian Processes for Multi-Agent Systems](https://mlsanity.com/paper/2502.05301/) (2025)
- [Decentralized Online Learning for Random Inverse Problems Over Graphs](https://mlsanity.com/paper/2303.11789/) (2023)
- [Statistical Theory of Multi-stage Newton Iteration Algorithm for Online Continual Learning](https://mlsanity.com/paper/2508.07419/) (2025)

## Abstract (arXiv)

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number of parameters as time iterations evolve. Besides complexity, this leads to an increased need of communication resources, in a distributed setting. In contrast, the proposed method approximates the solution as a fixed-size vector (of larger dimension than the input space) using Random Fourier Features. This paves the way to use standard linear combine-then-adapt techniques. To the best of our knowledge, this is the first time that a complete protocol for distributed online learning in RKHS is presented. Conditions for asymptotic convergence and boundness of the networkwise regret are also provided. The simulated tests illustrate the performance of the proposed scheme.