Treatment recommendation with distributional targets
This work addresses a decision-making problem in experimental settings where distributional targets are crucial, offering incremental improvements in policy design for scenarios like welfare optimization.
The paper tackles the problem of treatment recommendation when the goal is to optimize a distributional characteristic, such as inequality or welfare, rather than a simple average outcome, and shows that optimal recommendations may involve mixtures of treatments. It provides maximal expected regret lower bounds and proposes two near regret-optimal policies, one static and one sequential.
We study the problem of a decision maker who must provide the best possible treatment recommendation based on an experiment. The desirability of the outcome distribution resulting from the policy recommendation is measured through a functional capturing the distributional characteristic that the decision maker is interested in optimizing. This could be, e.g., its inherent inequality, welfare, level of poverty or its distance to a desired outcome distribution. If the functional of interest is not quasi-convex or if there are constraints, the optimal recommendation may be a mixture of treatments. This vastly expands the set of recommendations that must be considered. We characterize the difficulty of the problem by obtaining maximal expected regret lower bounds. Furthermore, we propose two (near) regret-optimal policies. The first policy is static and thus applicable irrespectively of subjects arriving sequentially or not in the course of the experimentation phase. The second policy can utilize that subjects arrive sequentially by successively eliminating inferior treatments and thus spends the sampling effort where it is most needed.