Toward Distributionally Robust Decision-Focused Learning

Decision-focused learning often relies on point predictions or decides under a single learned distribution, leaving downstream decisions vulnerable to model error. We propose a distributionally robust framework for decision-focused learning that learns a conditional distribution and conformally calibrates a Wasserstein ambiguity set around it. We use empirical Sinkhorn divergences as nonconformity scores, with corrections for entropic regularization and finite-sample estimation error. Under exchangeability and suitable concentration assumptions, the resulting Wasserstein-1 and squared Wasserstein-2 ambiguity sets contain the true conditional distribution with finite-sample marginal coverage. On the coverage event, the robust objective upper-bounds the true conditional expected task loss. We derive gradients through calibration and downstream optimization under regularity conditions, enabling end-to-end task-aware training. Experiments on portfolio allocation demonstrate improved decision quality over two-stage and stochastic decision-focused baselines.