Decision-making under uncertainty is a major challenge in operations research, especially when key data are only partly observed or subject to estimation errors. When the probability distribution of uncertain parameters is unknown, one typically relies on a finite historical dataset to infer plausible distributions. In this context, Wasserstein Distributionally Robust Optimization (WDRO) has become a powerful framework by its nice modeling and generalisation properties.
In this work, we study WDRO models involving combinatorial or discrete decision structures. We propose a tractable modelling approach based on the entropic regularization of the value function, which enables the computation of stochastic gradient estimators. To tackle the problem, we employ a stochastic Frank–Wolfe algorithm to optimise the WDRO objective while preserving the combinatorial nature of the constraints. This general approach expands the applicability of WDRO techniques to discrete optimization under uncertainty by bringing distributional robustness to scalable first-order methods.