  This paper studies the expected optimal value of a mixed 0-1 programming
problem with uncertain objective coefficients following a joint distribution.
We assume that the true distribution is not known exactly, but a set of
independent samples can be observed. Using the Wasserstein metric, we construct
an ambiguity set centered at the empirical distribution from the observed
samples and containing the true distribution with a high statistical guarantee.
The problem of interest is to investigate the bound on the expected optimal
value over the Wasserstein ambiguity set. Under standard assumptions, we
reformulate the problem into a copositive program, which naturally leads to a
tractable semidefinite-based approximation. We compare our approach with a
moment-based approach from the literature on three applications. Numerical
results illustrate the effectiveness of our approach.
