Data-driven inverse optimization seeks to estimate unknown parameters in an optimization model from observations of optimization solutions. Many existing methods are ineffective in handling noisy and suboptimal solution observations and also suffer from computational challenges. In this paper, we build a connection between inverse optimization and the Fenchel-Young (FY) loss originally designed for structured prediction, proposing a FY loss approach to data-driven inverse optimization. This new approach is amenable to efficient gradient-based optimization, hence much more efficient than existing methods. We provide theoretical guarantees for the proposed method and use extensive simulation and real-data experiments to demonstrate its significant advantage in parameter estimation accuracy, decision error and computational speed.

翻译：数据驱动逆向优化旨在通过观测优化方案的解来估计优化模型中的未知参数。许多现有方法在处理含噪声和次优解观测值方面效果不佳，且面临计算挑战。本文构建了逆向优化与最初为结构化预测设计的Fenchel-Young（FY）损失函数之间的关联，提出了一种基于FY损失函数的数据驱动逆向优化方法。该新方法适用于高效的梯度优化，因此比现有方法高效得多。我们为所提方法提供了理论保证，并通过大量仿真和真实数据实验证明了其在参数估计精度、决策误差及计算速度方面的显著优势。