Functional Sequential Treatment Allocation with Covariates

Document pages: 47 pages

Abstract: We consider a multi-armed bandit problem with covariates. Given a realizationof the covariate vector, instead of targeting the treatment with highestconditional expectation, the decision maker targets the treatment whichmaximizes a general functional of the conditional potential outcomedistribution, e.g., a conditional quantile, trimmed mean, or a socio-economicfunctional such as an inequality, welfare or poverty measure. We developexpected regret lower bounds for this problem, and construct a near minimaxoptimal assignment policy.