Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization
Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization
复制标题
DOI：
10.1016/j.compchemeng.2022.108123
复制
发表时间：
2022-10
期刊：
影响因子：
--
通讯作者：
Rishabh Gupta;Qi Zhang
中科院分区：
文献类型：
--
作者：
Rishabh Gupta;Qi Zhang
决策问题通常被表述为优化问题，然后对其进行求解以做出最优决策。在这项工作中，我们考虑了逆问题，其中我们使用先验决策数据以数学优化模型的形式揭示潜在的决策过程。这个统计学习问题被称为数据驱动的逆优化。我们关注的问题是，底层决策过程被建模为一个参数未知的凸优化问题。我们将反优化问题表述为一个双层程序，并提出了一种有效的基于块坐标下降的算法来解决大型问题实例。在合成数据集上的数值实验表明，与标准的商业求解器相比，我们的方法具有计算优势。此外，通过两个现实案例研究，我们考虑了多人纳什议价博弈中agent的风险偏好估计和局部约束参数学习，强调了所提出方法在现实世界中的实用性。
Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying decision-making process in the form of a mathematical optimization model. This statistical learning problem is referred to as data-driven inverse optimization. We focus on problems where the underlying decision-making process is modeled as a convex optimization problem whose parameters are unknown. We formulate the inverse optimization problem as a bilevel program and propose an efficient block coordinate descent-based algorithm to solve large problem instances. Numerical experiments on synthetic datasets demonstrate the computational advantage of our method compared to standard commercial solvers. Moreover, the real-world utility of the proposed approach is highlighted through two realistic case studies in which we consider estimating risk preferences and learning local constraint parameters of agents in a multiplayer Nash bargaining game.