Kernel-based function learning in dynamic and non stationary environments

TL;DR

This paper extends kernel-based ridge regression to non-stationary environments, providing convergence conditions for dynamic data distributions, which is crucial for adaptive monitoring and exploration tasks.

Contribution

It introduces convergence analysis for kernel ridge regression under non-stationary distributions, including scenarios with ongoing stochastic adaptation.

Findings

Derived convergence conditions for non-stationary data

Addressed infinite adaptation scenarios

Applicable to exploration-exploitation problems

Abstract

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.