We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon.
@article{arxiv.2109.06350,
title = {Controlling Unknown Linear Dynamics with Bounded Multiplicative Regret},
author = {Jacob Carruth and Maximilian F. Eggl and Charles Fefferman and Clarence W. Rowley and Melanie Weber},
journal= {arXiv preprint arXiv:2109.06350},
year = {2021}
}