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Title: Functional sequential treatment allocation Authors:  Bezirgen Veliyev - Aarhus University (Denmark) [presenting]
Anders Kock - Aarhus University and CREATES (Denmark)
David Preinerstorfer - Université libre de Bruxelles (Belgium)
Abstract: A treatment allocation problem with multiple treatments is studied, in which the individuals to be treated arrive sequentially. The quality of a treatment is allowed to be measured through a general (combination of) functionals of the underlying distribution of treatment outcomes, including inequality-, welfare- and poverty-measures. The goal of the policy maker is to minimize maximal expected regret compared to always assigning the unknown best treatment to all individuals. We first show that a natural approach to the policy maker's problem based on conducting an RCT to learn which treatment is best can incur very high maximal expected regret irrespective of the decision rule employed following the RCT. Motivated by this finding we study the Functional Upper Confidence Bound (FUCB) policy, which interweaves exploration and exploitation, and show that it performs better than any two-step policy based on an RCT. Furthermore, we show that, irrespective of the functional of interest, the expected regret incurred by the FUCB policy is near-minimax optimal. Next, we study the case of heterogeneous treatment outcome distributions by introducing covariates and show that the FUCB policy is minimax optimal over a broad class of treatment outcome distributions under minimal assumptions.