Mixed Integer Linear Programming For Exact FiniteHorizon Planning In Decentralized Pomdps
Abstract
We consider the problem of finding an nagent jointpolicy for the optimal finitehorizon control of a decentralized Pomdp (DecPomdp). This is a problem of very high complexity (NEXPhard in n >= 2). In this paper, we propose a new mathematical programming approach for the problem. Our approach is based on two ideas: First, we represent each agent's policy in the sequenceform and not in the treeform, thereby obtaining a very compact representation of the set of jointpolicies. Second, using this compact representation, we solve this problem as an instance of combinatorial optimization for which we formulate a mixed integer linear program (MILP). The optimal solution of the MILP directly yields an optimal jointpolicy for the DecPomdp. Computational experience shows that formulating and solving the MILP requires significantly less time to solve benchmark DecPomdp problems than existing algorithms. For example, the multiagent tiger problem for horizon 4 is solved in 72 secs with the MILP whereas existing algorithms require several hours to solve it.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 DOI:
 10.48550/arXiv.0707.2506
 arXiv:
 arXiv:0707.2506
 Bibcode:
 2007arXiv0707.2506A
 Keywords:

 Computer Science  Artificial Intelligence
 EPrint:
 Dans The International Conference on Automated Planning and Scheduling (2007)