Functional Sequential Treatment Allocation with Covariates
Machine Learning
2024-12-25 v1 Machine Learning
Econometrics
Statistics Theory
Statistics Theory
Abstract
We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socio-economic functional such as an inequality, welfare or poverty measure. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.
Cite
@article{arxiv.2001.10996,
title = {Functional Sequential Treatment Allocation with Covariates},
author = {Anders Bredahl Kock and David Preinerstorfer and Bezirgen Veliyev},
journal= {arXiv preprint arXiv:2001.10996},
year = {2024}
}
Comments
The material in this paper replaces the material on covariates in [v5] of "Functional Sequential Treatment Allocation"