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We study the distributed synthesis of policies for multi-agent systems toperform \emph{spatial-temporal} tasks. We formalize the synthesis problem as a\emph{factored} Markov decision process subject to \emph{graph temporal logic}specifications. The transition function and task of each agent are functions ofthe agent itself and its neighboring agents. In this work, we develop anotherdistributed synthesis method, which improves the scalability and runtime by twoorders of magnitude compared to our prior work. The synthesis method decomposesthe problem into a set of smaller problems, one for each agent by leveragingthe structure in the model, and the specifications. We show that the runningtime of the method is linear in the number of agents. The size of the problemfor each agent is exponential only in the number of neighboring agents, whichis typically much smaller than the number of agents. We demonstrate theapplicability of the method in case studies on disease control, urban security,and search and rescue. The numerical examples show that the method scales tohundreds of agents with hundreds of states per agent and can also handlesignificantly larger state spaces than our prior work.

Distributed Policy Synthesis of Multi-Agent Systems With Graph Temporal Logic Specifications