# Kernel-based function learning in dynamic and non stationary environments

arXiv: https://arxiv.org/abs/2310.02767 · HTML: https://mlsanity.com/paper/2310.02767/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 2 of 2)

- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [Boosting as a kernel-based method](https://mlsanity.com/paper/1608.02485/) (2016)

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

- [Gaussian kernel expansion with basis functions uniformly bounded in L∞](https://mlsanity.com/paper/2410.01394/) (2024)

## Abstract (arXiv)

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the last decades, a substantial amount of work has been devoted to design estimators for the unknown function and to study their convergence to the optimal predictor, also characterizing the learning rate. These results typically rely on stationary assumptions where input locations are drawn from a probability distribution that does not change in time. In this work, we consider kernel-based ridge regression and derive convergence conditions under non stationary distributions, addressing also cases where stochastic adaption may happen infinitely often. This includes the important exploration-exploitation problems where e.g. a set of agents/robots has to monitor an environment to reconstruct a sensorial field and their movements rules are continuously updated on the basis of the acquired knowledge on the field and/or the surrounding environment.