发表机构
Center for Control, Dynamical Systems, and Computation, UC Santa Barbara（加州大学圣塔芭芭拉分校控制、动力学与计算中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出提升马尔可夫链作为智能体巡逻策略的新范式，证明其性能优于非提升马尔可夫链，提供优化方法并通过仿真验证其在稀疏图上的显著改进。
AI 中文摘要
本文提出提升马尔可夫链（MC）作为一种新范式，用于推导在以图表示的环境中移动智能体的巡逻策略。提升马尔可夫链的状态空间可大于图的节点集合，且存在投影操作将马尔可夫链状态映射到图的对应节点。我们证明了提升马尔可夫链相较于非提升马尔可夫链的性能提升边界，其中性能以Kemeny常数衡量，并展示了对应的Stackelberg博弈捕获概率与返回时间熵的单调性。这些边界得出了一个具有独立意义的结果，即关联了一般马尔可夫链的Kemeny常数与电导。我们还提供了一种可处理的方法，用于在边权编码旅行时间的一般图上优化提升马尔可夫链。在随机生成图与真实世界图上的仿真结果验证，提升马尔可夫链实现了显著改进，尤其在稀疏图上表现突出。
英文摘要
In this paper we propose lifted Markov Chains (MCs) as a new paradigm for deriving patrol strategies for mobile agents on an environment represented as a graph. Lifted MCs operate on a state space that can be larger than the set of nodes of the graph, and a projection operation maps the MC state to the corresponding node of the graph. We prove bounds on the performance improvement of lifted MCs over non-lifted MCs, where the performance is measured by the Kemeny constant, and show a corresponding monotonicity for the Stackelberg game capture probability and return-time entropy. These bounds yield a result of independent interest that relates the Kemeny constant and the MC conductance for general MCs. We also provide a tractable method for optimizing lifted MCs on general graphs with edge weights encoding travel times. Simulation results on randomly generated and real-world graphs verify that lifted MCs achieve substantial improvements, particularly on sparse graphs.
Comments14 pages, 8 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible
