A Fenchel-Young Loss Approach to Data-Driven Inverse Optimization

• URL: http://arxiv.org/abs/2502.16120v2
• Date: Wed, 02 Apr 2025 07:14:40 GMT
• Title: A Fenchel-Young Loss Approach to Data-Driven Inverse Optimization
• Authors: Zhehao Li, Yanchen Wu, Xiaojie Mao,
• Abstract summary: We build a connection between inverse optimization and the Fenchel-Young (FY) loss originally designed for structured prediction.<n>This new approach is amenable to efficient gradient-based optimization, hence much more efficient than existing methods.
• Score: 1.7068557927955381
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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