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

A Data-Driven Distributionally Robust Bound on the Expected Optimal Value of Uncertain Mixed 0-1 Linear Programming