Optimal sequential treatment allocation

In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the uncertainty/risk of the treatment outcomes. At the outset, the total number of treatment assignments to be made may even be unknown. A sequential treatment policy which attains the minimax optimal regret is proposed. We also demonstrate that the expected number of suboptimal treatments only grows slowly in the number of treatments. Finally, we study a setting where outcomes are only observed with delay.