标题： 基于数据驱动的拦截与不对称成本不确定性：一种分布鲁棒优化方法 显示英文标题

标题： Data-driven interdiction with asymmetric cost uncertainty: a distributionally robust optimization approach

摘要： 我们考虑一个由上层决策者（称为领导者）和下层决策者（称为跟随者）之间的随机干扰博弈组成的类别，其中不确定性存在于跟随者的目标函数系数中。 具体而言，我们模型中跟随者的利润（或成本）包括一个随机向量，其概率分布由领导者和跟随者根据各自的数据独立估计。 为了解决分布不确定性，我们制定了一个分布鲁棒的干扰（DRI）模型，其中两个决策者都基于Wasserstein度量解决传统的分布鲁棒优化问题。 对于该模型，我们证明了渐近一致性，并推导出一个多项式规模的混合整数线性规划（MILP）重写形式。 此外，在我们的双层优化背景下，由于领导者对跟随者数据的不完全了解，可能会面临不确定性。 在这方面，我们提出了两个不同的真实DRI模型的近似方法，其中领导者对跟随者数据的信息不完整或没有信息。 第一种方法采用了一种悲观近似，这被证明在计算上具有挑战性，并需要设计一种专门的Benders分解算法。 第二种方法从领导者的角度利用了一种鲁棒优化方法。 为了解决由此产生的问题，我们提出了一种基于情景的外逼近方法，该方法可以接受潜在的大规模单层MILP重写形式，并满足渐近鲁棒性保证。 最后，对于一类随机生成的装箱干扰问题实例，我们数值评估了信息不对称和决策者风险偏好如何影响模型的样本外性能。 显示英文摘要

摘要： We consider a class of stochastic interdiction games between an upper-level decision-maker (referred to as a leader) and a lower-level decision-maker (referred to as a follower), where uncertainty lies in the follower's objective function coefficients. Specifically, the follower's profits (or costs) in our model comprise a random vector, whose probability distribution is estimated independently by the leader and the follower, based on their own data. To address the distributional uncertainty, we formulate a distributionally robust interdiction (DRI) model, where both decision-makers solve conventional distributionally robust optimization problems based on the Wasserstein metric. For this model, we prove asymptotic consistency and derive a polynomial-size mixed-integer linear programming (MILP) reformulation. Furthermore, in our bilevel optimization context, the leader may face uncertainty due to its incomplete knowledge of the follower's data. In this regard, we propose two distinct approximations of the true DRI model, where the leader has incomplete or no information about the follower's data. The first approach employs a pessimistic approximation, which turns out to be computationally challenging and requires the design of a specialized Benders decomposition algorithm. The second approach leverages a robust optimization approach from the leader's perspective. To address the resulting problem, we propose a scenario-based outer approximation that admits a potentially large single-level MILP reformulation and satisfies asymptotic robustness guarantees. Finally, for a class of randomly generated instances of the packing interdiction problem, we evaluate numerically how the information asymmetry and the decision-makers' risk preferences affect the models' out-of-sample performance.