Data-Driven Approximation of Contextual Chance-Constrained Stochastic Programs
针对经典随机规划忽略多维特征依赖的问题，提出一种融入特征的上下文机会约束规划模型，并给出数据驱动近似方法，在疫苗分配问题中验证了其可行性。
.Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, and we propose a tractable and fully data-driven approximate model that relies on weighted sums of random variables. We obtain a stochastic lower bound for the optimal value and feasibility results that include convergence to the true feasible set as the number of data points increases, as well as the minimal number of data points needed to obtain a feasible solution with high probability. We illustrate our findings in a vaccine allocation problem and compare the results with a naïve sample average approximation approach.Keywordschance constraintsdata-driven optimizationstochastic programminglarge deviationsMSC codes90C1590C3990C47