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

TL;DR

This paper introduces a Fenchel-Young loss-based method for data-driven inverse optimization that improves efficiency and accuracy, especially with noisy or suboptimal data, supported by theoretical guarantees and extensive experiments.

Contribution

It proposes a novel Fenchel-Young loss approach to inverse optimization, enabling efficient gradient-based training and improved parameter estimation.

Findings

Significant improvement in parameter estimation accuracy

Faster computational speed compared to existing methods

Effective handling of noisy and suboptimal observations

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.