Under sign conditions on the technology matrix, the worst-case expected recourse cost in two-stage distributionally robust programs with infinity-Wasserstein ambiguity is exactly a finite linear or conic program with explicit penalty terms.
Two-stage sample robust optimization
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abstract
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result establishes that this approximation scheme is asymptotically optimal for two-stage stochastic linear optimization problems; that is, under mild assumptions, the optimal cost and optimal first-stage decisions obtained by approximating the robust optimization problem converge to those of the underlying stochastic problem as the number of data points grows to infinity. These guarantees notably apply to two-stage stochastic problems that do not have relatively complete recourse, which arise frequently in applications. In this context, we show through numerical experiments that the approximation scheme is practically tractable and produces decisions which significantly outperform those obtained from state-of-the-art data-driven alternatives.
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2019 1verdicts
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Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty-$Wasserstein Distance
Under sign conditions on the technology matrix, the worst-case expected recourse cost in two-stage distributionally robust programs with infinity-Wasserstein ambiguity is exactly a finite linear or conic program with explicit penalty terms.