  This manuscript introduces the idea of using Distributionally Robust
Optimization (DRO) for the Counterfactual Risk Minimization (CRM) problem.
Tapping into a rich existing literature, we show that DRO is a principled tool
for counterfactual decision making. We also show that well-established
solutions to the CRM problem like sample variance penalization schemes are
special instances of a more general DRO problem. In this unifying framework, a
variety of distributionally robust counterfactual risk estimators can be
constructed using various probability distances and divergences as uncertainty
measures. We propose the use of Kullback-Leibler divergence as an alternative
way to model uncertainty in CRM and derive a new robust counterfactual
objective. In our experiments, we show that this approach outperforms the
state-of-the-art on four benchmark datasets, validating the relevance of using
other uncertainty measures in practical applications.
