Robust Decision-Focused Learning via Worst-Case Regret Minimization

In optimization-based decision-making, when the objective coefficient vector is unknown, a common approach is to predict it from covariates using a machine learning model and solve the downstream optimization problem. However, improving predictive accuracy does not necessarily lead to better decisions. This has motivated Decision-Focused Learning (DFL), which trains predictive models to minimize decision loss measured by regret. Despite recent progress, existing DFL methods do not sufficiently address two sources of uncertainty: (i) observation errors in the measured coefficients, and (ii) distribution shift in the coefficient vector at deployment due to environmental changes. These uncertainties can degrade solution quality. In this paper, we propose two robust regret losses to address these uncertainties. For uncertainty (i), we introduce an uncertainty set around the observed coefficient vector that captures measurement errors and define the loss as the worst-case regret over this set. For uncertainty (ii), we construct a {Wasserstein} ambiguity set around the conditional empirical distribution and define the loss using the worst-case distribution within the set. We enable efficient training via Danskin-based subgradients. Experiments demonstrate that our method reduces regret and yields more stable solutions than existing robust DFL approaches.