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.

翻译：在这项工作中,我们考虑了一个逆向问题,即我们利用先前的决策数据,以数学优化模式的形式发现基本决策过程。这种统计学习问题被称为数据驱动的反向优化。我们集中关注以下问题:基本决策过程模拟为一个参数未知的共振优化问题。我们将优化问题作为一个双级方案,提出一个反向问题,并提出一个高效的组合协调基于世系的算法,以解决大问题。合成数据集的量化实验显示了我们方法与标准商业解决方案相比的计算优势。此外,通过两个现实的案例研究,我们考虑估算风险偏好和学习多玩家纳什讨价还价游戏中代理商的当地约束参数,从而突显了拟议方法在现实世界中的效用。