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. Thus, we allow the welfare function to depend on the first and second moments of the distribution of treatment outcomes. We propose a dynamic treatment  policy which attains the minimax optimal regret relative to the unknown best treatment in this dynamic setting. We allow for the data to arrive in batches as, say, unemployment programs only start once a month or blood samples are only send to the laboratory for investigation in batches. Furthermore, we show that the minimax optimality does not come at the price of overly aggressive experimentation as we provide upper bounds on the expected number of times any suboptimal treatment is assigned. We also consider the case where the outcome of a treatment is only observed with delay as it may take time for the treatment to work. Thus, a doctor faces a tradeoff between getting imprecise information quickly by making the measurement soon after the treatment is given or getting precise information later at the expense of less information for the individuals who are treated in the meantime . Finally, using Danish register data, we show how our treatment policy can be used to assign unemployed to active labor market policy programs in order to maximise the probability of ending the unemployment spell .
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 .
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a treatment allocation problem
treatment allocation problems
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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
sequentially. We study a problem in which the policy maker is not only
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effect
cumulative welfare but is also concerned about the uncertainty/risk
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but also its riskiness. Thus, we allow the welfare function to depend on the first and second moments of the distribution of treatment
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We propose a dynamic
At the outset, the total number of
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assignments to be made may even be unknown. A sequential treatment
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relative to the unknown best treatment in this dynamic setting. We allow for the data to arrive in batches as, say, unemployment programs only start once a month or blood samples are only send to the laboratory for investigation in batches. Furthermore, we show that the minimax optimality does not come at the price of overly aggressive experimentation as we provide upper bounds on the
is proposed. We also demonstrate that the
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times any suboptimal treatment is assigned. We also consider the case where the outcome of a treatment is only observed with delay as it may take time for the treatment to work. Thus, a doctor faces a tradeoff between getting imprecise information quickly by making the measurement soon after the treatment is given or getting precise information later at the expense of less information for the individuals who are treated in the meantime
suboptimal treatments only grows slowly in the number of treatments
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using Danish register data, we show how our treatment policy can be used to assign unemployed to active labor market policy programs in order to maximise the probability of ending the unemployment spell
we study a setting where outcomes are only observed with delay