A Fenchel-Young Loss Approach to Data-Driven Inverse Optimization
Zhehao Li, Yanchen Wu, Xiaojie Mao
TL;DR
The paper tackles data-driven inverse optimization in the presence of noisy observations by linking inverse optimization to the Fenchel-Young loss. It introduces a regularized forward optimization (R-FOP) framework and shows that the Fenchel-Young loss provides a differentiable, convex surrogate with a closed-form gradient under linear costs, enabling efficient gradient-based optimization. The authors establish calibration bounds and statistical guarantees connecting the excess Fenchel-Young risk to decision and parameter errors, and they demonstrate superior performance and scalability through extensive synthetic and real-data experiments, notably on Uber Movement data. The work yields practical improvements in parameter estimation, decision quality, and computational speed, and it opens avenues for further applying FY loss to broad inverse-optimization settings and nonlinear forward models.
Abstract
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.