Functional Sequential Treatment Allocation with Covariates

• URL: http://arxiv.org/abs/2001.10996v1
• Date: Wed, 29 Jan 2020 18:08:53 GMT
• Title: Functional Sequential Treatment Allocation with Covariates
• Authors: Anders Bredahl Kock, David Preinerstorfer, Bezirgen Veliyev
• Abstract summary: Decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution. We develop expected regret lower bounds for this problem, and construct a near minimax optimal assignment policy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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