论文标题

在不确定性下具有上下文信息的二重性框架,用于决策

A bilevel framework for decision-making under uncertainty with contextual information

论文作者

Muñoz, Miguel Angel, Pineda, Salvador, Morales, Juan Miguel

论文摘要

在本文中,我们提出了一种新的方法,用于在存在上下文信息的情况下在不确定性下进行数据驱动的决策。考虑到对不确定参数和潜在解释变量(即上下文信息)的观察有限的收集,我们的方法符合参数模型,适合那些专门针对最大化决策值的数据,同时考虑了可能的可行性约束。从数学的角度来看,我们的框架转化为一个双重程序,为此我们提供了快速的正则化过程和基于M的大型重新印象,可以使用现成的优化求解器来解决。我们展示了使用三个不同的实际问题从传统方案(基于统计质量指标)转变为决策引导预测的好处。我们还将我们的方法与现有案例研究中的现有方法进行了比较,该案例研究考虑了参与伊比利亚电力市场的战略发电商。最后,我们使用这些数值仿真来分析我们的方法对生产者更有利的条件(根据公司的成本结构和生产能力)。

In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically tailored to maximizing the decision value, while accounting for possible feasibility constraints. From a mathematical point of view, our framework translates into a bilevel program, for which we provide both a fast regularization procedure and a big-M-based reformulation that can be solved using off-the-shelf optimization solvers. We showcase the benefits of moving from the traditional scheme for model estimation (based on statistical quality metrics) to decision-guided prediction using three different practical problems. We also compare our approach with existing ones in a realistic case study that considers a strategic power producer that participates in the Iberian electricity market. Finally, we use these numerical simulations to analyze the conditions (in terms of the firm's cost structure and production capacity) under which our approach proves to be more advantageous to the producer.

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