  I study the problem of a decision maker choosing a policy which allocates
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 by shape restrictions on treatment
response. Policies are compared according to the minimax regret criterion, and
I show that the empirical analog of the population decision problem has a
tractable linear- and integer-programming formulation. I prove the maximum
regret of the estimated policy converges to the lowest possible maximum regret
at a rate which is the maximum of N^-1/2 and the rate at which conditional
average treatment effects are estimated in the experimental data. 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.
