We study the distributed synthesis of policies for multi-agent systems to perform spatial-temporal tasks. We formalize the synthesis problem as a factored Markov decision process subject to graph temporal logic specifications. The transition function and task of each agent is a function of the agent itself and its neighboring agents. By leveraging the structure in the model, and the specifications, we develop a distributed algorithm that decomposes the problem into a set of smaller problems, one for each agent. We show that the running time of the algorithm is linear in the number of agents. The size of the problem for each agent is exponential only in the number of neighboring agents, which is typically much smaller than the number of agents. If the transition function of each agent does not depend on its neighboring agents, we show that we can simplify the algorithm, which improves the runtime by multiple orders of magnitude. We demonstrate the algorithms in case studies on disease control, urban security, and ground robot surveillance. The numerical examples show that the algorithms can scale to hundreds of agents with hundreds of states per agent.

中文翻译：

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具有图时序逻辑规范的多代理系统的分布式策略合成

我们研究了多代理系统执行时空任务的策略的分布式综合。我们将综合问题形式化为受制于图时间逻辑规范的分解马尔可夫决策过程。每个代理的转换函数和任务是代理本身及其相邻代理的函数。通过利用模型中的结构和规范，我们开发了一种分布式算法，将问题分解为一组较小的问题，每个代理一个。我们表明算法的运行时间与代理的数量呈线性关系。每个代理的问题规模仅与相邻代理的数量呈指数关系，这通常远小于代理的数量。如果每个智能体的转移函数不依赖于它的相邻智能体，我们表明我们可以简化算法，从而将运行时间提高多个数量级。我们在疾病控制、城市安全和地面机器人监视的案例研究中展示了算法。数值例子表明算法可以扩展到数百个代理，每个代理有数百个状态。