Online Conditional Robust Optimization with Conformal Robustness Control

We study online conditional robust optimization, where decisions are made by minimizing worst-case loss over prediction sets before the true labels are observed. Existing online conformal prediction methods can ensure long-run decision robustness under arbitrary distribution shifts, but may yield overly conservative decisions because predictive coverage is sufficient but not necessary for robustness. To address this issue, we propose Online Conformal Robustness Control (OCRC), which formulates this task as an online constrained learning problem, minimizing average worst-case loss on past observations subject to an explicit robustness constraint. OCRC dynamically updates prediction-set thresholds directly from feedback on past robustness violations. We establish long-run robustness control for arbitrary data sequences and asymptotically exact marginal robustness under stochastic data settings. Experiments on synthetic and real-world data show that OCRC maintains the target robustness level while achieving substantially lower decision risks than coverage-based methods.