Estimation of Subsidiary Performance Metrics under Optimal Policies

In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention.This paper presents two strategies for evaluating these subsidiary metrics under a policy that is optimal for the primary one.The first relies on a novel margin condition that facilitates Wald-type inference.Under this and other regularity conditions, we show that the one-step corrected estimator is e cient.Despite the utility of this margin condition, it places strong restrictions on how the subsidiary metric behaves for nearly-optimal policies, which may not hold in practice.We therefore introduce alternative, two-stage strategies that do not require a margin condition.The first stage constructs a set of candidate policies and the second builds a uniform confidence interval over this set.We provide numerical simulations to evaluate the performance of these methods in dierent scenarios.