Contrastive Explanations of 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 $P$?''. In this paper, we propose MAoE, a domain-independent approach to obtain contrastive explanations by (i) generating a new solution $S^\prime$ where the property $P$ is enforced, while also minimizing the differences between $S$ and $S^\prime$; and (ii) highlighting the differences between the two solutions. Such explanations aim to help agents understanding why the initial solution is better than what they expected. We have carried out a computational evaluation that shows that MAoE 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, after being presented with these explanations, humans' satisfaction with the original solution increases.