  We consider the problem of learning from training data obtained in different
contexts, where the underlying context distribution is unknown and is estimated
empirically. We develop a robust method that takes into account the uncertainty
of the context distribution. Unlike the conventional and overly conservative
minimax approach, we focus on excess risks and construct distribution sets with
statistical coverage to achieve an appropriate trade-off between performance
and robustness. The proposed method is computationally scalable and shown to
interpolate between empirical risk minimization and minimax regret objectives.
Using both real and synthetic data, we demonstrate its ability to provide
robustness in worst-case scenarios without harming performance in the nominal
scenario.
