Planning for Cooperative Multiple Agents with Sparse Interaction Constraints

We consider the problem of cooperative multi-agent planning (MAP) in a deterministic environment, with a completely observable state. Most tractable algorithms for MAP problems assume sparse interactions among agents and exploitable problem structure. We consider a specific model for representing interactions among agents using soft cooperation constraints (SCC), which enables a compact representation of symmetric dependencies. We present a two-step planning algorithm that breaks down a multi-agent problem with K agents, to multiple instances of independent single-agent problems, such that the aggregation of the single-agent plans is optimal for the group. We propose an efficient algorithm for computing the single-agent optimal plan under a given set of soft constraints, denoted as the response function. We then utilize a well-known graphical model for efficient min-sum optimization in order to find the optimal aggregation of the single agent response functions. The proposed planning algorithm is complete, optimal, and effective when interactions among the agents are sparse. We further indicate some useful extensions to the basic SCC formulation presented here.