# Adaptation and learning over networks for nonlinear system modeling

## TL;DR

This paper explores distributed nonlinear system modeling, emphasizing the distinction between single-task and multitask problems, and introduces a kernel-based algorithm for multitask scenarios evaluated on a benchmark.

## Contribution

It introduces a simple kernel-based algorithm tailored for multitask nonlinear system modeling in distributed environments, addressing a gap in existing literature.

## Key findings

- The proposed algorithm performs well on simulated benchmark tasks.
- Multitask modeling offers advantages over single-task approaches in distributed settings.
- Open problems and future research directions are discussed.

## Abstract

In this chapter, we analyze nonlinear filtering problems in distributed environments, e.g., sensor networks or peer-to-peer protocols. In these scenarios, the agents in the environment receive measurements in a streaming fashion, and they are required to estimate a common (nonlinear) model by alternating local computations and communications with their neighbors. We focus on the important distinction between single-task problems, where the underlying model is common to all agents, and multitask problems, where each agent might converge to a different model due to, e.g., spatial dependencies or other factors. Currently, most of the literature on distributed learning in the nonlinear case has focused on the single-task case, which may be a strong limitation in real-world scenarios. After introducing the problem and reviewing the existing approaches, we describe a simple kernel-based algorithm tailored for the multitask case. We evaluate the proposal on a simulated benchmark task, and we conclude by detailing currently open problems and lines of research.