Silva Thuener, Valladão Davi, Homem-de-Mello Tito
Industrial Engineering Department, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rua Marquês de São Vicente, 225, Gávea , Rio de Janeiro, RJ 22451-900 Brazil.
School of Business, Universidad Adolfo Ibáñez, Diagonal las Torres 2640, Peñalolén, Santiago Chile.
Comput Optim Appl. 2021;80(3):687-729. doi: 10.1007/s10589-021-00320-4. Epub 2021 Sep 28.
Dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use statistical predictive methods to capture the structure of the underlying stochastic process without taking into consideration estimation errors and model misspecification. In this context, we propose a data-driven prescriptive analytics framework aiming to integrate the machine learning and dynamic optimization machinery in a consistent and efficient way to build a bridge from data to decisions. The proposed framework tackles a relevant class of dynamic decision problems comprising many important practical applications. The basic building blocks of our proposed framework are: (1) a Hidden Markov Model as a predictive (machine learning) method to represent uncertainty; and (2) a distributionally robust dynamic optimization model as a prescriptive method that takes into account estimation errors associated with the predictive model and allows for control of the risk associated with decisions. Moreover, we present an evaluation framework to assess out-of-sample performance in rolling horizon schemes. A complete case study on dynamic asset allocation illustrates the proposed framework showing superior out-of-sample performance against selected benchmarks. The numerical results show the practical importance and applicability of the proposed framework since it extracts valuable information from data to obtain robustified decisions with an empirical certificate of out-of-sample performance evaluation.
动态随机优化模型提供了一个强大的工具来表示序贯决策过程。通常情况下，这些模型使用统计预测方法来捕捉潜在随机过程的结构，而不考虑估计误差和模型误设。在此背景下，我们提出了一个数据驱动的规范分析框架，旨在以一致且高效的方式整合机器学习和动态优化机制，从而搭建起从数据到决策的桥梁。所提出的框架解决了一类包含许多重要实际应用的动态决策问题。我们所提出框架的基本组成部分包括：（1）一个隐马尔可夫模型作为一种预测（机器学习）方法来表示不确定性；以及（2）一个分布鲁棒动态优化模型作为一种规范方法，该方法考虑了与预测模型相关的估计误差，并允许对与决策相关的风险进行控制。此外，我们提出了一个评估框架，以评估滚动时域方案中的样本外性能。一个关于动态资产配置的完整案例研究展示了所提出的框架，其相对于选定的基准表现出卓越的样本外性能。数值结果表明了所提出框架的实际重要性和适用性，因为它从数据中提取有价值的信息，以获得具有样本外性能评估实证证明的稳健决策。
