Gittins' theorem under uncertainty
Optimization and Control
2021-06-16 v3 Probability
Statistics Theory
Computational Finance
Statistics Theory
Abstract
We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involves studying the interaction of our uncertainty with controls which determine the filtration. We also run a simple numerical example which illustrates the interaction between the willingness to explore and uncertainty aversion of the agent when making decisions.
Cite
@article{arxiv.1907.05689,
title = {Gittins' theorem under uncertainty},
author = {Samuel N. Cohen and Tanut Treetanthiploet},
journal= {arXiv preprint arXiv:1907.05689},
year = {2021}
}