Mixed Integer Linear Programming For Exact Finite-Horizon Planning In
  Decentralized Pomdps
  We consider the problem of finding an n-agent joint-policy for the optimal
finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem
of very high complexity (NEXP-hard 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 sequence-form and not in
the tree-form, thereby obtaining a very compact representation of the set of
joint-policies. 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 joint-policy for the Dec-Pomdp. Computational experience
shows that formulating and solving the MILP requires significantly less time to
solve benchmark Dec-Pomdp problems than existing algorithms. For example, the
multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP
whereas existing algorithms require several hours to solve it.
