Algorithms for secure patrols in adversarial domains

We consider the problem of providing decision support to a patrolling or security service in an adversarial domain. The idea is to create patrols that can achieve a high level of coverage or reward while taking into account the presence of an adversary. We assume that the adversary can learn or observe the patrolling strategy and use this to its advantage. We follow two different approaches depending on what is known about the adversary. If there is no information about the adversary we use a Markov Decision Process (MDP) to represent patrols and identify randomized solutions that minimize the information available to the adversary. This leads to algorithm BRLP, for policy randomization of MDPs. Second, when there is partial information about the adversary we decide on efficient patrols by solving a Bayesian Stackelberg game. Here, the leader decides first on a patrolling strategy and then an adversary, of possibly many adversary types, selects its best response for the given patrol. We provide an efficient MIP formulation to solve this NP-hard problem. Our experimental results show the efficiency of these algorithms and illustrate how these techniques provide optimal and secure patrolling policies.