Before revision: In a treatment allocation problem the individuals to be treated often arrive gradually. Initially, when the first treatments are made, little is known about the effect of the treatments but as more treatments are assigned the policy maker learns about their effects by observing outcomes. Thus, there is a tradeoff between exploring the available treatments to learn about their merits and exploiting the best treatment, i.e. administering it as often as possible, in order to maximise the cumulative welfare of all the assignments made. Furthermore, a policy maker may not only be interested in the expected effect of the treatment but also its riskiness.
After revision: In a treatment allocation problem the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected effect of the treatment but also its riskiness.