  This paper extends the Distributionally Robust Optimization (DRO) approach
for offline contextual bandits. Specifically, we leverage this framework to
introduce a convex reformulation of the Counterfactual Risk Minimization
principle. Besides relying on convex programs, our approach is compatible with
stochastic optimization, and can therefore be readily adapted tothe large data
regime. Our approach relies on the construction of asymptotic confidence
intervals for offline contextual bandits through the DRO framework. By
leveraging known asymptotic results of robust estimators, we also show how to
automatically calibrate such confidence intervals, which in turn removes the
burden of hyper-parameter selection for policy optimization. We present
preliminary empirical results supporting the effectiveness of our approach.
