Non-approximability of Decentralized Control

The complexity of finding an optimal decentralized policy for a cooperative multi-agent system is known to be non-deterministically exponential. Agents in such a system try to maximize a single global utility function, and do not compete; nevertheless, computing the optimal strategies for these agents is intractable. In this paper, we relax the requirement of finding an optimal decentralized policy for a cooperative multiagent system. We consider, instead, the complexity of finding decentralized policy solutions whose values are -distant from the optimal solution value, i.e., sub-optimal solutions that may have errors. Among the major contributions of this research is showing that the apparently easier problem of finding an approximate solution to decentralized control remains as hard as the optimal version of the problem. This paper, by formally analyzing the complexity of finding optimal and sub-optimal joint policies for cooperative decentralized systems, sheds new light on the theoretical foundations of multiagent systems. In particular, we have adopted from complexity theory the concept of multiprover interactive protocols (MIPs), which can serve as computational models for certain kinds of multi-agent systems. This is a new direction not yet studied within the distributed artificial intelligence community, one that provides new opportunities for the theoretical analysis of multiagent systems.