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In this work, we consider a cooperative multi-agent Markov decision process(MDP) involving m agents. At each decision epoch, all the m agentsindependently select actions in order to maximize a common long-term objective.In the policy iteration process of multi-agent setup, the number of actionsgrows exponentially with the number of agents, incurring huge computationalcosts. Thus, recent works consider decentralized policy improvement, where eachagent improves its decisions unilaterally, assuming that the decisions of theother agents are fixed. However, exact value functions are considered in theliterature, which is computationally expensive for a large number of agentswith high dimensional state-action space. Thus, we propose approximatedecentralized policy iteration algorithms, using approximate linear programmingwith function approximation to compute the approximate value function fordecentralized policy improvement. Further, we consider (both) cooperativemulti-agent finite and infinite horizon discounted MDPs and propose suitablealgorithms in each case. Moreover, we provide theoretical guarantees for ouralgorithms and also demonstrate their advantages over existing state-of-the-artalgorithms in the literature.

Approximate Linear Programming for Decentralized Policy Iteration in Cooperative Multi-agent Markov Decision Processes