# Contrastive Explanations of Centralized Multi-agent Optimization Solutions

arXiv: https://arxiv.org/abs/2308.05984 · HTML: https://mlsanity.com/paper/2308.05984/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [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)
- [Metrics for Explainable AI: Challenges and Prospects](https://mlsanity.com/paper/1812.04608/) (2018)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [Contrastive Explanations of Plans Through Model Restrictions](https://mlsanity.com/paper/2103.15575/) (2021)
- [AI for Explaining Decisions in Multi-Agent Environments](https://mlsanity.com/paper/1910.04404/) (2019)
- [Understanding Consumer Preferences for Explanations Generated by XAI Algorithms](https://mlsanity.com/paper/2107.02624/) (2021)
- [Explaining Preference-driven Schedules: the EXPRES Framework](https://mlsanity.com/paper/2203.08895/) (2022)

## Built on by (most cited first, 4 of 4)

- [On Generating Monolithic and Model Reconciling Explanations in Probabilistic Scenarios](https://mlsanity.com/paper/2405.19229/) (2024)
- [Contrastive Explainable Clustering with Differential Privacy](https://mlsanity.com/paper/2406.04610/) (2024)
- [TRACE-CS: A Hybrid Logic-LLM System for Explainable Course Scheduling](https://mlsanity.com/paper/2409.03671/) (2024)
- [Exploiting Constraint Reasoning to Build Graphical Explanations for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2507.13007/) (2025)

## Abstract (arXiv)

In many real-world scenarios, agents are involved in optimization problems. Since most of these scenarios are over-constrained, optimal solutions do not always satisfy all agents. Some agents might be unhappy and ask questions of the form ``Why does solution S not satisfy property P?''. We propose CMAoE, a domain-independent approach to obtain contrastive explanations by: (i) generating a new solution S^prime where property P is enforced, while also minimizing the differences between S and S^prime; and (ii) highlighting the differences between the two solutions, with respect to the features of the objective function of the multi-agent system. Such explanations aim to help agents understanding why the initial solution is better in the context of the multi-agent system than what they expected. We have carried out a computational evaluation that shows that CMAoE can generate contrastive explanations for large multi-agent optimization problems. We have also performed an extensive user study in four different domains that shows that: (i) after being presented with these explanations, humans' satisfaction with the original solution increases; and (ii) the constrastive explanations generated by CMAoE are preferred or equally preferred by humans over the ones generated by state of the art approaches.