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In this work, we consider a `cooperative' multi-agent Markov decision process(MDP) involving m greater than 1 agents, where all agents are aware of thesystem model. At each decision epoch, all the m agents cooperatively selectactions in order to maximize a common long-term objective. Since the number ofactions grows exponentially in the number of agents, policy improvement iscomputationally expensive. Recent works have proposed using decentralizedpolicy improvement in which each agent assumes that the decisions of the otheragents are fixed and it improves its decisions unilaterally. Yet, in theseworks, exact values are computed. In our work, for cooperative multi-agentfinite and infinite horizon discounted MDPs, we propose suitable approximatepolicy iteration algorithms, wherein we use approximate linear programming tocompute the approximate value function and use decentralized policyimprovement. Thus our algorithms can handle both large number of states as wellas multiple agents. We provide theoretical guarantees for our algorithms andalso demonstrate the performance of our algorithms on some numerical examples.

Approximate Linear Programming and Decentralized Policy Improvement in Cooperative Multi-agent Markov Decision Processes