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This research addresses the exponential complexity inherent in decentralized partially observable Markov decision processes (DecPOMDPs) by shifting from agent counting to policy counting, thereby enabling tractable solutions for multi-agent systems under uncertainty. The proposed method utilizes compact representations and dynamic programming to efficiently solve these problems despite a large policy space, offering significant improvements over traditional approaches that struggle with scaling agent numbers.
The Curious Case of Exploding DecPOMDPs: Containing the Fire through Policy Counting
arXiv:2608.17749v1 Announce Type: new Abstract: Decentralised partially observable Markov decision processes (DecPOMDPs) provide a general framework for modelling multi-agent decision making under uncertainty. However, DecPOMDPs are known to suffer from exponential complexity in the number of agents. One way to combat this intractability in agent numbers is to look at partitions of agents that exhibit a form of symmetry among agents, allowing for a compact encoding by counting. However, a challenge arises as the policy space explodes, even though the model complexity and evaluation cost reduce to a polynomial dependence. In this paper, we redirect our focus from counting agents to counting policies, which actually enables tractability in agent numbers for so called policy-counted DecPOMDPs. Further, we present policy-counted dynamic programming using the compact representation to solve policy-counted DecPOMDPs efficiently.
Abstract:Decentralised partially observable Markov decision processes (DecPOMDPs) provide a general framework for modelling multi-agent decision making under uncertainty. However, DecPOMDPs are known to suffer from exponential complexity in the number of agents. One way to combat this intractability in agent numbers is to look at partitions of agents that exhibit a form of symmetry among agents, allowing for a compact encoding by counting. However, a challenge arises as the policy space explodes, even though the model complexity and evaluation cost reduce to a polynomial dependence. In this paper, we redirect our focus from counting agents to counting policies, which actually enables tractability in agent numbers for so called policy-counted DecPOMDPs. Further, we present policy-counted dynamic programming using the compact representation to solve policy-counted DecPOMDPs efficiently.
Artificial Intelligence (cs.AI)
arXiv:2608.17749 [cs.AI]
(or arXiv:2608.17749v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.17749 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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