题目：Contextual Chance-Constrained Programs: A Lifted L∞ Optimal Transport Approach

主讲人：王曙明（中国科学院大学）

时间：3月26日 15：30-16：30

地点：红宝石活动优惠大厅hbs大楼318会议室

摘要：

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 lifts an L∞ 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∞-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 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 valid inequalities, and a Benders decomposition scheme that exploits the decomposability of the lifted L∞-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.

主讲人简介：

王曙明：国科大经管学院教授、院长助理、博士生导师。研究方向：预测驱动型最优化、鲁棒优化、统计与计量学习及其在运筹管理的应用。研究成果发表于管理科学著名期刊 Operations Research，Production and Operations Management以及INFORMS Journal on Computing等。目前担任“中国管理现代化研究会”理事，“中国优选法统筹法与经济数学研究会-风险管理分会”常务理事以及“中国运筹学会-决策科学分会”常务理事。担任Elsevier旗下运筹学著名国际期刊Computers & Operations Research部门主编，同时担任决策科学旗舰期刊Decision Sciences副主编以及运营管理著名期刊Production and Operations Management编委。