Reflected Fenchel-Young Conformal Calibration for Decision-Aware Contextual Robust Optimization

Conformal prediction is commonly used to construct uncertainty sets for contextual robust optimization. However, residual-based calibration can enlarge these sets in response to prediction errors that do not affect the optimal decision, inducing unnecessary conservatism. This motivates calibrating the regret of the nominal decision directly. However, we show that, under regularity conditions, minimizing worst-case regret over the resulting regret set uniquely recovers the nominal decision, so robust optimization leaves the decision unchanged. We address this limitation using reflected Fenchel-Young (FY) conformal scores for convex optimization with linear objective uncertainty. The score provides a richer characterization of decision performance, admitting an exact decomposition into nominal regret, the suboptimality of the hindsight optimizer under the prediction, and a reflected stability gap. Split conformal calibration gives finite-sample marginal guarantees. We further characterize when the calibrated set improves worst-case regret and develop a master-pricing algorithm with optimality certificates. Experiments confirm the predicted self-centering phenomenon and show that reflected FY refinement improves decision quality over residual-based robust baselines in portfolio and real-data solar-grid allocation problems.