When Are Kalman-Filter Restless Bandits Indexable?
Abstract
We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is {\it indexable} in the sense that the {\it Whittle index} is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about {\it Schur-convexity} and {\it mechanical words}, which are particularbinary strings intimately related to {\it palindromes}.
Cite
Text
Dance and Silander. "When Are Kalman-Filter Restless Bandits Indexable?." Neural Information Processing Systems, 2015.Markdown
[Dance and Silander. "When Are Kalman-Filter Restless Bandits Indexable?." Neural Information Processing Systems, 2015.](https://mlanthology.org/neurips/2015/dance2015neurips-kalmanfilter/)BibTeX
@inproceedings{dance2015neurips-kalmanfilter,
title = {{When Are Kalman-Filter Restless Bandits Indexable?}},
author = {Dance, Christopher R and Silander, Tomi},
booktitle = {Neural Information Processing Systems},
year = {2015},
pages = {1711-1719},
url = {https://mlanthology.org/neurips/2015/dance2015neurips-kalmanfilter/}
}