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：数据驱动逆优化旨在通过观测优化问题的解来估计优化模型中的未知参数。现有许多方法在处理含噪声及次优解观测时效果不佳，同时也面临计算上的挑战。本文建立了逆优化与最初为结构化预测设计的Fenchel-Young损失之间的联系，提出了一种基于Fenchel-Young损失的数据驱动逆优化方法。这一新方法适用于高效的基于梯度的优化算法，因此计算效率远高于现有方法。我们为所提方法提供了理论保证，并通过大量仿真与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。