Sensitivity analysis for distributed optimization with resource constraints

Previous work in multiagent coordination has addressed the challenge of planning in domains where agents must optimize a global goal, while satisfying local resource constraints. However, the imposition of resource constraints naturally raises the question of whether the agents could significantly improve their team performance if a few more resources were made available. Sensitivity analysis aims to answer that question. This paper focuses on sensitivity analysis in the context of the distributed coordination framework, Multiply-Constrained DCOP (MC-DCOP). There are three main challenges in performing sensitivity analysis: (i) to perform it in a distributed fashion, (ii) to avoid re-solving an NP-hard MC-DCOP optimization from scratch, and (iii) to avoid considering unproductive uses for extra resources. To meet these challenges, this paper presents three types of locally optimal algorithms: link analysis, local reoptimization and local constraint propagation. These algorithms are distributed and avoid redundant computation by ascertaining just the effects of local perturbations on the original problem. Deploying our algorithms on a large number of MC-DCOP problems revealed several results. While our cheapest algorithm successfully identified quality improvements for a few problems, our more complex techniques were necessary to identify the best uses for additional resources. Furthermore, we identified two heuristics that can help identify a priori which agents might benefit most from additional resources: density rank, which works well when nodes received identical resources and remaining resource rank, which works well when nodes received resources based on the number of neighbors they had.