Policy Learning with New Treatments

I study the problem of a decision maker choosing a policy to allocate treatment to a heterogeneous population on the basis of experimental data that includes only a subset of possible treatment values. The effects of new treatments are partially identified based on shape restrictions on treatment response. I propose solving an empirical minimax regret problem to estimate the policy and show it has a tractable linear- and integer-programming formulation. I prove the maximum regret of the estimator converges to the lowest possible maximum regret at the rate at which heterogeneous treatment effects can be estimated in the experimental data or $N^{-1/2}$, whichever is slower. I apply my results to design targeted subsidies for electrical grid connections in rural Kenya, and estimate that $97\%$ of the population should be given a treatment not implemented in the experiment