Policy Counting Tames Complexity in Multi-Agent DecPOMDPs

Decentralised Partially Observable Markov Decision Processes (DecPOMDPs) are a powerful framework for modeling decision-making in multi-agent systems under uncertainty. However, their practical application is severely hampered by an exponential increase in complexity as the number of agents grows. While previous attempts to manage this intractability have focused on exploiting agent symmetries through counting, this often leads to an explosion in the policy space, despite reducing model complexity. This research proposes a novel approach by redirecting the focus from counting agents to counting policies. By introducing "policy-counted DecPOMDPs," the paper demonstrates how this shift can enable tractability even with a large number of agents. Furthermore, it presents a policy-counted dynamic programming method that leverages this compact representation to efficiently solve these complex multi-agent decision problems.