论文标题
在分布强劲的多阶段凸优化方面：数据驱动的模型和性能
On Distributionally Robust Multistage Convex Optimization: Data-driven Models and Performance
论文作者
论文摘要
本文提出了一项新的算法研究，并通过分布强大的多阶段凸优化（DR-MCO）进行了广泛的数值实验。在先前关于DR-MCO的双重动态编程（DDP）算法框架的工作之后，我们将重点放在数据驱动的DR-MCO模型上，并具有Wasserstein模棱两可的集合，允许使用无限支持的概率度量。这些数据驱动的Wasserstein DR-MCO模型具有样本外的性能保证和可调节的样本保守主义。然后，通过利用不确定成本功能中的其他凹度或凸度，我们设计了确切的单阶段子问题Oracle（SSSO）实现，以确保DDP算法的收敛性。我们测试了数据驱动的WASSERSTEIN DR-MCO模型，可针对多阶段鲁棒凸优化（MRCO），风险中性和规避风险的多阶段多阶段随机凸优化（MSCO）模型（MSCO）模型，这些模型涉及多商品库存问题以及水力热功率计划问题。结果表明，当数据大小很小时，我们的DR-MCO模型可以胜过MRCO和MSCO模型。
This paper presents a novel algorithmic study with extensive numerical experiments of distributionally robust multistage convex optimization (DR-MCO). Following the previous work on dual dynamic programming (DDP) algorithmic framework for DR-MCO, we focus on data-driven DR-MCO models with Wasserstein ambiguity sets that allow probability measures with infinite supports. These data-driven Wasserstein DR-MCO models have out-of-sample performance guarantees and adjustable in-sample conservatism. Then by exploiting additional concavity or convexity in the uncertain cost functions, we design exact single stage subproblem oracle (SSSO) implementations that ensure the convergence of DDP algorithms. We test the data-driven Wasserstein DR-MCO models against multistage robust convex optimization (MRCO), risk-neutral and risk-averse multistage stochastic convex optimization (MSCO) models on multi-commodity inventory problems and hydro-thermal power planning problems. The results show that our DR-MCO models could outperform MRCO and MSCO models when the data size is small.
