Explainable Distributed Constraint Optimization Problems

TL;DR

This work addresses the explainability gap in distributed constraint optimization by introducing X-DCOP, which augments a DCOP with a solution and a contrastive query to generate grounded, cost-based explanations. It proposes the CEDAR distributed framework to compute valid contrastive explanations, along with optimizations and suboptimal variants that trade explanation length for runtime. The authors establish existence results for valid explanations under k-optimality and demonstrate scalability up to 50 agents, plus a human study showing users prefer concise explanations. By bridging explainable AI with distributed optimization, the work enables more transparent and adoptable DCOP-based solutions in real-world multi-agent systems.

Abstract

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.

Figures (31)

• Figure 1: Example DCOP.
• Figure 2: When Receive REQUEST($a_Q$, $\bar{\sigma}_Q$)
• Figure 3: When Receive REPLY($a_i$, $\bar{\sigma}_Q$, ${\bf{F}}^{a_i}_{\downarrow \bar{\sigma}_Q}$)
• Figure 4: Experimental results for CEDAR, its optimized versions, and its variants on meeting scheduling problems with $10$ meetings for optimal complete solutions; solid lines denote results for best alternative queries and dashed lines denote results for random queries.
• Figure 5: Percentage of instances for which valid explanations were found using CEDAR (O1) as a function of query variables $|{\textit{var}(\sigma_Q)}|$ with $|\mathcal{A}| = 10$ on 1-opt and optimal solutions for meeting scheduling problems.

Theorems & Definitions (3)

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