Title: Welfare maximizing dynamic treatment allocation and recommendation
Authors: Anders Kock - Aarhus University and CREATES (Denmark)
David Preinerstorfer - Université libre de Bruxelles (Belgium)
Bezirgen Veliyev - Aarhus University (Denmark) [presenting]
Abstract: In many decision problems information arrives gradually. For example, patients with a certain illness arrive gradually to the hospital and information about competing treatments accumulates as patients are treated. The hospital thus faces a tradeoff between exploring the merits of the available treatments and administering the optimal treatment as often as possible. We cast this problem as a multi-armed bandit problem and develop treatment algorithms that are optimal in the sense that no other algorithm can incur a smaller loss in terms of rates. Furthermore, we show that by the end of the treatment period we can give a recommendation on the best treatment which is not much worse than if this treatment had been known. We take into account that the optimal treatment may be person specific and that one may not only target the treatment with the highest expected effect as its risk may also be of interest. More precisely, we show minimax optimality of our treatment algorithm even when targeting quite general functionals of the distribution of treatment outcomes. These functionals include quantiles and smooth functions of a finite number of moments of the treatment outcomes.