  A decision-maker faces uncertainty governed by a data-generating process
(DGP), which is only known to belong to a set of sequences of independent but
possibly non-identical distributions. A robust decision maximizes the expected
payoff against the worst possible DGP in this set. This paper characterizes
when and how such robust decisions can be improved with data, measured by the
expected payoff under the true DGP, no matter which possible DGP is the truth.
It further develops novel and simple inference methods to achieve it, as common
methods (e.g., maximum likelihood) may fail to deliver such an improvement.
