The Complexity of Decentralized Control of Markov Decision Processes

TL;DR

This paper investigates the computational complexity of decentralized control in Markov Decision Processes, revealing that such problems are inherently much harder than their centralized counterparts, likely requiring doubly exponential time to solve.

Contribution

It introduces generalized models for decentralized MDPs and POMDPs and proves their planning problems are complete for nondeterministic exponential time, highlighting fundamental complexity differences.

Findings

Decentralized control problems are complete for nondeterministic exponential time.

These problems do not admit polynomial-time algorithms and are likely doubly exponential.

Decentralized planning cannot be easily reduced to centralized solutions.

Abstract

Planning for distributed agents with partial state information is considered from a decision- theoretic perspective. We describe generalizations of both the MDP and POMDP models that allow for decentralized control. For even a small number of agents, the finite-horizon problems corresponding to both of our models are complete for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov processes. In contrast to the MDP and POMDP problems, the problems we consider provably do not admit polynomial-time algorithms and most likely require doubly exponential time to solve in the worst case. We have thus provided mathematical evidence corresponding to the intuition that decentralized planning problems cannot easily be reduced to centralized problems and solved exactly using established techniques.