Abstract
We present a novel strategy for a patroller defending a set of heterogeneous assets from the attacks carried by an attacker that through repeated observations attempts to learn the strategy followed by the patroller. Implemented through a Markov chain whose stationary distribution is a function of the values of the assets being defended and the topology of the environment, the strategy is biased towards providing more protection to valuable assets, yet is provably hard to learn for an opponent. After having studied its properties, we show that our proposed method outperforms strategies commonly used for this type of problems.
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Notes
- 1.
The assumption is w.l.o.g. since any non-complete graph can be turned into a complete one by taking its closure on shortest paths, i.e., adding an edge \((l_i,l_j)\) and setting \(d_{i,j}\) to the cost of the shortest path between \(l_i\) and \(l_j\) in the original graph.
- 2.
This simplified version is obtained assuming that the proposal distribution is \(\frac{1}{n}\) for all i, j. See [14] for more details.
- 3.
The density must be 0 for values smaller than \(d_{i,j}\) because the patroller must generate a time larger than the minimum time necessary to complete the move.
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Basilico, N., Carpin, S. (2020). Balancing Unpredictability and Coverage in Adversarial Patrolling Settings. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_44
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