基于图时态逻辑规范的因子化MDP策略综合
Policy Synthesis for Factored MDPs with Graph Temporal Logic Specifications
摘要：
我们研究了多智能体系统实现时空任务的策略合成。我们正式的问题作为一个因素马尔可夫决策过程受到所谓的图形时序逻辑规范。每个智能体的转移功能和时空任务取决于智能体本身及其邻近的智能体。在模型和规格的结构，使开发一个分布式算法，给定一个因子马尔可夫决策过程和图形时序逻辑公式，分解成一组较小的合成问题，每个代理的合成问题。我们证明了该算法运行在时间上的总代理数的线性。每个代理的合成问题的大小仅在相邻代理的数量上是指数的，这通常比代理的数量小得多。我们在疾病控制和城市安全的案例研究中证明了该算法。数值算例表明，该算法可以扩展到数百个智能体。
英文摘要：
We study the synthesis of policies for multi-agent systems to implement spatial-temporal tasks. We formalize the problem as a factored Markov decision process subject to so-called graph temporal logic specifications. The transition function and the spatial-temporal task of each agent depend on the agent itself and its neighboring agents. The structure in the model and the specifications enable to develop a distributed algorithm that, given a factored Markov decision process and a graph temporal logic formula, decomposes the synthesis problem into a set of smaller synthesis problems, one for each agent. We prove that the algorithm runs in time linear in the total number of agents. The size of the synthesis problem for each agent is exponential only in the number of neighboring agents, which is typically much smaller than the number of agents. We demonstrate the algorithm in case studies on disease control and urban security. The numerical examples show that the algorithm can scale to hundreds of agents.
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