# Counterfactual Explanations Using Optimization With Constraint Learning

arXiv: https://arxiv.org/abs/2209.10997 · HTML: https://mlsanity.com/paper/2209.10997/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 21 of 21)

- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Learning in High Dimension Always Amounts to Extrapolation](https://mlsanity.com/paper/2110.09485/) (2021)
- [Inverse Classification for Comparison-based Interpretability in Machine Learning](https://mlsanity.com/paper/1712.08443/) (2017)
- [Global Deterministic Optimization with Artificial Neural Networks Embedded](https://mlsanity.com/paper/1801.07114/) (2018)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [BRPO: Batch Residual Policy Optimization](https://mlsanity.com/paper/2002.05522/) (2020)
- [Learning optimization models in the presence of unknown relations](https://mlsanity.com/paper/1401.1061/) (2014)
- [Optimal Counterfactual Explanations for Scorecard modelling](https://mlsanity.com/paper/2104.08619/) (2021)

## Built on by (most cited first, 8 of 8)

- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Generating collective counterfactual explanations in score-based classification via mathematical optimization](https://mlsanity.com/paper/2310.12822/) (2023)
- [Causal Inference for Banking Finance and Insurance A Survey](https://mlsanity.com/paper/2307.16427/) (2023)
- [Counterfactual Explanations for Linear Optimization](https://mlsanity.com/paper/2405.15431/) (2024)
- [Clinicians' Voice: Fundamental Considerations for XAI in Healthcare](https://mlsanity.com/paper/2411.04855/) (2024)
- [Supervised Feature Compression based on Counterfactual Analysis](https://mlsanity.com/paper/2211.09894/) (2022)
- [T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems](https://mlsanity.com/paper/2309.16146/) (2023)
- [Improving understanding and trust in AI: How users benefit from interval-based counterfactual explanations](https://mlsanity.com/paper/2604.09573/) (2026)

## Abstract (arXiv)

To increase the adoption of counterfactual explanations in practice, several criteria that these should adhere to have been put forward in the literature. We propose counterfactual explanations using optimization with constraint learning (CE-OCL), a generic and flexible approach that addresses all these criteria and allows room for further extensions. Specifically, we discuss how we can leverage an optimization with constraint learning framework for the generation of counterfactual explanations, and how components of this framework readily map to the criteria. We also propose two novel modeling approaches to address data manifold closeness and diversity, which are two key criteria for practical counterfactual explanations. We test CE-OCL on several datasets and present our results in a case study. Compared against the current state-of-the-art methods, CE-OCL allows for more flexibility and has an overall superior performance in terms of several evaluation metrics proposed in related work.