The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model cooperative multi-agent problems that need to be solved distributively. A core assumption of existing approaches is that DCOP solutions can be easily understood, accepted, and adopted, which may not hold, as evidenced by the large body of literature on Explainable AI. In this paper, we propose the Explainable DCOP (X-DCOP) model, which extends a DCOP to include its solution and a contrastive query for that solution. We formally define some key properties that contrastive explanations must satisfy for them to be considered as valid solutions to X-DCOPs as well as theoretical results on the existence of such valid explanations. To solve X-DCOPs, we propose a distributed framework as well as several optimizations and suboptimal variants to find valid explanations. We also include a human user study that showed that users, not surprisingly, prefer shorter explanations over longer ones. Our empirical evaluations showed that our approach can scale to large problems, and the different variants provide different options for trading off explanation lengths for smaller runtimes. Thus, our model and algorithmic contributions extend the state of the art by reducing the barrier for users to understand DCOP solutions, facilitating their adoption in more real-world applications.

Learning-to-rank (LTR) is a class of supervised learning techniques that apply to ranking problems dealing with a large number of features. The popularity and widespread application of LTR models in prioritizing information in a variety of domains makes their scrutability vital in today's landscape of fair and transparent learning systems. However, limited work exists that deals with interpreting the decisions of learning systems that output rankings. In this paper we propose a model agnostic local explanation method that seeks to identify a small subset of input features as explanation to a ranking decision. We introduce new notions of validity and completeness of explanations specifically for rankings, based on the presence or absence of selected features, as a way of measuring goodness. We devise a novel optimization problem to maximize validity directly and propose greedy algorithms as solutions. In extensive quantitative experiments we show that our approach outperforms other model agnostic explanation approaches across pointwise, pairwise and listwise LTR models in validity while not compromising on completeness.