Conformal Robustness in Prediction-Driven Decision-Making

Point forecasts from black-box predictors lack a calibrated scale for downstream robust optimization. We develop a score-calibrated interface for any predictor, using the conformal score rather than an uncertainty set as the robustness unit. Its calibrated sublevel sets support reliability-based conformal robust optimization (ConfRO), while the same score normalizes target violations in Conformal Robust Satisficing (ConfRS). We derive finite-sample decision and target certificates, an efficiency bound separating calibration radius from decision sensitivity, and an axiomatic fragility measure. For convex programs with objective uncertainty, exact score duality yields a set-valued ConfRO–ConfRS frontier and a reliability–target translation. Local smoothness yields marginal-cost formulas for robustness and reliability. Fractional-knapsack experiments demonstrate calibrated coverage, utility gains over robust baselines, and the predicted frontier structure.