Conformal Robustness Control: A New Strategy for Robust Decision

Robust decision-making is crucial in numerous risk-sensitive applications where outcomes are uncertain and the cost of failure is high. Conditional Robust Optimization (CRO) offers a framework for such tasks by constructing prediction sets for the outcome that satisfy predefined coverage requirements and then making decisions based on these sets. Many existing approaches leverage conformal prediction to build prediction sets with guaranteed coverage for CRO. However, since coverage is a sufficient but not necessary condition for robustness, enforcing such constraints often leads to overly conservative decisions. To overcome this limitation, we propose a novel framework named Conformal Robustness Control (CRC), that directly optimizes the prediction set construction under explicit robustness constraints, thereby enabling more efficient decisions without compromising robustness. We develop efficient algorithms to solve the CRC optimization problem, and also provide theoretical guarantees on both robustness and optimality. Empirical results show that CRC consistently yields more effective decisions than existing baselines while still meeting the target robustness level.