Faster Rates for Policy Learning
Abstract
This article improves the existing proven rates of regret decay in optimal policy estimation. We give a margin-free result showing that the regret decay for estimating a within-class optimal policy is second-order for empirical risk minimizers over Donsker classes, with regret decaying at a faster rate than the standard error of an efficient estimator of the value of an optimal policy. We also give a result from the classification literature that shows that faster regret decay is possible via plug-in estimation provided a margin condition holds. Four examples are considered. In these examples, the regret is expressed in terms of either the mean value or the median value; the number of possible actions is either two or finitely many; and the sampling scheme is either independent and identically distributed or sequential, where the latter represents a contextual bandit sampling scheme.
Cite
@article{arxiv.1704.06431,
title = {Faster Rates for Policy Learning},
author = {Alexander Luedtke and Antoine Chambaz},
journal= {arXiv preprint arXiv:1704.06431},
year = {2017}
}