Regularizing fairness in optimal policy learning with distributional targets

A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an “optimal” predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being “unfair” against a subgroup of the population, in the sense that the outcome distribution in that subgroup deviates too strongly from the overall optimal outcome distribution. We study a framework that allows the decision maker to regularize such deviations, while allowing for a wide range of target functionals and fairness measures to be employed. We establish regret and consistency guarantees for empirical success policies with (possibly) data-driven preference parameters, and provide numerical results. Furthermore, we briefly illustrate the methods in two empirical settings.