  We study the empirical likelihood approach to construct confidence intervals
for the optimal value and the optimality gap of a given solution, henceforth
quantify the statistical uncertainty of sample average approximation, for
optimization problems with expected value objectives and constraints where the
underlying probability distributions are observed via limited data. This
approach relies on two distributionally robust optimization problems posited
over the uncertain distribution, with a divergence-based uncertainty set that
is suitably calibrated to provide asymptotic statistical guarantees.
