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

## TL;DR

This paper introduces a novel distributed online learning method in RKHS using Random Fourier Features, enabling fixed-size parameter updates and reducing communication complexity in networked environments.

## Contribution

It presents the first complete protocol for distributed online learning in RKHS with fixed-size approximations using Random Fourier Features.

## Key findings

- Achieves convergence and bounded network regret.
- Demonstrates effective performance in simulations.
- Reduces communication overhead in distributed settings.

## Abstract

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.