Conformal Inverse Optimization

TL;DR

This paper introduces conformal inverse optimization, a method that learns uncertainty sets for unknown parameters to improve decision quality and alignment with human intuition, with theoretical guarantees and strong empirical results.

Contribution

It proposes a novel conformal inverse optimization approach that constructs uncertainty sets for parameters, enhancing decision robustness and interpretability over traditional inverse optimization.

Findings

Provides theoretical guarantees on solution quality.

Demonstrates superior empirical performance.

Ensures decisions are aligned with human intuition.

Abstract

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters are used to prescribe new decisions. The prescribed decisions may be low-quality and misaligned with human intuition and thus are unlikely to be adopted. To tackle this challenge, we propose conformal inverse optimization, which seeks to learn an uncertainty set for the unknown parameters and then solve a robust optimization model to prescribe new decisions. Under mild assumptions, we show that our method enjoys provable guarantees on solution quality, as evaluated using both the ground-truth parameters and the decision maker's perception of the unknown parameters. Our method demonstrates strong empirical performance compared to classic inverse optimization.