Recovering Predictions without Regretting Decisions: Cone-constrained Prediction Recovery for Decision-Focused Learning

Decision-Focused Learning (DFL) often improves decision quality at the expense of prediction accuracy, commonly read as an inherent trade-off. Exact regret depends on a prediction only through its induced decision, so poor accuracy can reflect unclaimed degrees of freedom rather than a cost that decision quality requires, and adding prediction error to the training objective does not isolate this freedom because it can also change which decision is selected. We propose Cone-constrained Prediction Recovery (CPR), which refines a trained predictor within anchored subsets of the optimality cones of its base decisions by solving one convex quadratic program. The trained predictor is itself a candidate solution of this program, so its prediction error cannot increase, and with unique base solutions and strict anchoring the decisions and their regret are preserved. Across five DFL methods, CPR substantially reduces prediction error while leaving regret nearly unchanged.