Learning to steer with Brownian noise
Machine Learning
2024-10-07 v1 Machine Learning
Probability
Statistics Theory
Statistics Theory
Abstract
This paper considers an ergodic version of the bounded velocity follower problem, assuming that the decision maker lacks knowledge of the underlying system parameters and must learn them while simultaneously controlling. We propose algorithms based on moving empirical averages and develop a framework for integrating statistical methods with stochastic control theory. Our primary result is a logarithmic expected regret rate. To achieve this, we conduct a rigorous analysis of the ergodic convergence rates of the underlying processes and the risks of the considered estimators.
Cite
@article{arxiv.2410.03221,
title = {Learning to steer with Brownian noise},
author = {Stefan Ankirchner and Sören Christensen and Jan Kallsen and Philip Le Borne and Stefan Perko},
journal= {arXiv preprint arXiv:2410.03221},
year = {2024}
}