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arXiv · 2610.10903

Deceptive Stochastic Patrolling via Markov Chain Lifting

Yohan John·Gilberto Diaz-Garcia·Jason R. Marden·Francesco Bullo
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Abstract

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.

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Yohan John, Gilberto Diaz-Garcia, Jason R. Marden, Francesco Bullo. 2026-10-07. Deceptive Stochastic Patrolling via Markov Chain Lifting. https://arxiv.org/abs/2610.10903

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