题　目：Contextual Chance-Constrained Programs: A Lifted $L^\infty$ Optimal Transport Approach

嘉　宾：王曙明 教授 中国科学院大学

主持人：许欢 教授 上海交通大学安泰经济与管理学院

时　间：2025年3月26日（周三）10:00-11:30

地　点：安泰楼B207室

内容简介：

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 paper, 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 \textit{lifts｝an $L^\infty$ optimal transport (OT) counterpart and houses a general multivariate regression model with correlated errors. Under several regularity conditions, we show that the solution of the proposed lifted $L^\infty$-OT based contextual model remains feasible with high probability under the true distribution of uncertainty. In particular, the worst-case chance converges to the true underlying counterpart at a {\it polynomial｝ rate with respect to both dimensions of the random parameters and the contextual covariates, which provides attractive finite-sample feasibility guarantees and asymptotic consistency for our model solution. Furthermore, we extend the framework to incorporate a non-parametric kernel regression approach, deriving additional finite-sample performance guarantees. 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 \textit{valid inequalities｝, and a Benders decomposition scheme that exploits the \textit{decomposability｝ of the lifted $L^\infty$-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.

演讲人简介：

Dr. Shuming Wang is a Professor of Management Science at the School of Economics and Management, University of Chinese Academy of Sciences (UCAS). His research interests include predictive data-driven analytics with applications in location science, transportation, supply chain management, and healthcare operations. He has published more than 30 papers including those in Operations Research, Production and Operations Management, INFORMS Journal on Computing, and Transportation Science. He serves as an Area Editor at Computers & Operations Research and an Associate Editor at Decision Sciences.

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