Contrastive Explanations of Centralized Multi-agent Optimization Solutions

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.