# Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

arXiv: https://arxiv.org/abs/1908.02376 · HTML: https://mlsanity.com/paper/1908.02376/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2019.

## Built on by (most cited first, 6 of 6)

- [Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization](https://mlsanity.com/paper/2210.15393/) (2022)
- [Scalable Kernel Inverse Optimization](https://mlsanity.com/paper/2410.23952/) (2024)
- [Inverse Bayesian Optimization: Learning Human Acquisition Functions in an Exploration vs Exploitation Search Task](https://mlsanity.com/paper/2104.09237/) (2021)
- [Social-Inverse: Inverse Decision-making of Social Contagion Management with Task Migrations](https://mlsanity.com/paper/2209.10493/) (2022)
- [Neural Quantile Optimization for Edge-Cloud Networking](https://mlsanity.com/paper/2307.05170/) (2023)
- [Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimization](https://mlsanity.com/paper/2606.28764/) (2026)

## Abstract (arXiv)

Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and corresponding forward solutions from the existing inverse LP method can be highly sensitive to noise, errors, and uncertainty in the input data, limiting its applicability in data-driven settings. We introduce the notion of inverse and forward stability in inverse LP and propose a novel inverse LP method that determines a set of objective functions that are stable under data imperfection and generate solutions close to the relevant subset of the data. We formulate the inverse model as a mixed-integer program and elucidate its connection to bi-clique problems, which we exploit to develop efficient heuristics. We also show how this method can be used for online learning. We numerically evaluate the stability of the proposed method and demonstrate its practical use in the diet recommendation and transshipment applications.