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

arXiv: https://arxiv.org/abs/2502.16120 · HTML: https://mlsanity.com/paper/2502.16120/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 22 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Data-Driven Estimation in Equilibrium Using Inverse Optimization](https://mlsanity.com/paper/1308.3397/) (2013)
- [Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms](https://mlsanity.com/paper/1805.09717/) (2018)
- [Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit](https://mlsanity.com/paper/1511.04650/) (2015)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Generalized Inverse Optimization through Online Learning](https://mlsanity.com/paper/1810.01920/) (2018)
- [Learning Energy Networks with Generalized Fenchel-Young Losses](https://mlsanity.com/paper/2205.09589/) (2022)
- [Inverse Optimization of Convex Risk Functions](https://mlsanity.com/paper/1607.07099/) (2016)
- [A Data-driven Bidding Model for a Cluster of Price-responsive Consumers of Electricity](https://mlsanity.com/paper/1506.06587/) (2015)
- [Short-term Forecasting of Price-responsive Loads Using Inverse Optimization](https://mlsanity.com/paper/1607.07209/) (2016)
- [Forecasting the Price-Response of a Pool of Buildings via Homothetic Inverse Optimization](https://mlsanity.com/paper/2004.09819/) (2020)
- [Trade-off preservation in inverse multi-objective convex optimization](https://mlsanity.com/paper/1706.06926/) (2017)

## Abstract (arXiv)

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.