Chance-constrained programming (CCP), as an important class of optimization-under-uncertainty models, has been employed in many high-stakes decision-making problems. In this work, we study a contextual robust model of joint CCP with piece-wise convex constraints of uncertain coefficients and binary decision variables. To harness contextual information for boosting decision performance with appealing statistical guarantees, and to improve solution scalability, we develop a predictive ambiguity set that lifts an L-infinity optimal transport (OT) counterpart and houses a nonparametric kernel regression model. Under several regularity conditions, we show that the solution of the proposed lifted L-infinity-OT based contextual model remains feasible with high probability under the true distribution of uncertainty. Optimization-wise, we develop exact solution methods for the proposed framework, tailored to commonly used OT cost functions. These include a reformulation scheme of mixed-integer conic program that exploits linearization with derived valid inequalities, and a Benders decomposition scheme that exploits the decomposability of the lifted L-infinity-OT model to enhance the scalability. Finally, we validate the model's robustness, the value of capturing contextual information, its finite-sample performance, and its computational efficiency through a redundancy allocation testing problem using both simulated and real-world datasets.

Li Jun is a Ph.D. candidate in the Department of Industrial Systems Engineering and Management, National University of Singapore, under the supervision of Prof. Ng Tsan Sheng, Adam. He obtained the Bachelor’s degree in Statistics from Southeast University and the Master’s degree in Management Science and Engineering from University of Chinese Academy of Sciences. His research interests include data-driven optimization and decision-making under uncertainty.