An Investigation into Mathematical Programming for Finite Horizon Decentralized POMDPs

Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, sol...

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Bibliographic Details
Published in:The Journal of artificial intelligence research Vol. 37; pp. 329 - 396
Main Authors: Aras, R., Dutech, A.
Format: Journal Article
Language:English
Published: San Francisco AI Access Foundation 01.01.2010
Association for the Advancement of Artificial Intelligence
Subjects:
Algorithms
Artificial Intelligence
Combinatorial analysis
Complexity
Computer Science
Decision theory
Dynamic programming
Game theory
Integer programming
Linear programming
Markov processes
Mathematical programming
Mixed integer
Representations
Decentralized Process
Multiagent Systems
Dynamic Programming
Artificial Intelligence
Mathematical Programming
ISSN:1076-9757, 1076-9757, 1943-5037
Online Access:Get full text
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Summary:Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, solving them is a task with an overwhelming complexity that can be doubly exponential. In this paper, we study an alternate formulation of DEC-POMDPs relying on a sequence-form representation of policies. From this formulation, we show how to derive Mixed Integer Linear Programming (MILP) problems that, once solved, give exact optimal solutions to the DEC-POMDPs. We show that these MILPs can be derived either by using some combinatorial characteristics of the optimal solutions of the DEC-POMDPs or by using concepts borrowed from game theory. Through an experimental validation on classical test problems from the DEC-POMDP literature, we compare our approach to existing algorithms. Results show that mathematical programming outperforms dynamic programming but is less efficient than forward search, except for some particular problems. The main contributions of this work are the use of mathematical programming for DEC-POMDPs and a better understanding of DEC-POMDPs and of their solutions. Besides, we argue that our alternate representation of DEC-POMDPs could be helpful for designing novel algorithms looking for approximate solutions to DEC-POMDPs.
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ISSN:1076-9757
1076-9757
1943-5037
DOI:10.1613/jair.2915