Combining Graph Contraction and Strategy Generation for Green Security Games

Basak, Anjon; Fang, Fei; Nguyen, Thanh H.; Kiekintveld, Christopher

doi:10.1007/978-3-319-47413-7_15

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…The branching strategy we employed is a rather standard one. Given node B, we first compute the quantities: measuring the error of McCormick underestimator for each bilinear term x i y i at the optimal solution of the relaxed problem (5). Then, we select r ∈ arg max i=1,…,n g i , i.e., the index corresponding to the bilinear term where we have the largest error at the optimal solution of the relaxation.…”

Section: Branchingmentioning

confidence: 99%

“…Note that all choices above, with the new McCormick relaxation given by the new limits on the variables, reduce to zero the error for bilinear term x r y r at the optimal solution of problem (5). It is worthwhile to remark that the computed lower bound tends to become exact even when branching is always performed with respect to variables of the same type (say, always variables x i , i = 1, … , n ).…”

Section: } Respectively (Quaternary Branching); Branching On Xmentioning

confidence: 99%

“…Note that games of a shape like that of our police patrolling example exist in manifold versions in the literature, such as regarding the patrolling of coast guards [10], border patrol [21], pipeline protection [3], airport surveillance [22], and game theoretic models against environmental crime (so-called green security games) [5]; see [28] for a more extensive overview of related game models. Common to all these is their goal of optimizing patrolling (and to an extent also surveillance), but none of this past work accounts for the efforts of realizing the patrolling in practice, in light of the efforts practically invested (for the moving), but not theoretically counted in the optimization model.…”

Section: Example: Crime Prevention By Patrolling (Of the Police)mentioning

confidence: 99%

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Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems

et al. 2021

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In this paper we address game theory problems arising in the context of network security. In traditional game theory problems, given a defender and an attacker, one searches for mixed strategies which minimize a linear payoff functional. In the problems addressed in this paper an additional quadratic term is added to the minimization problem. Such term represents switching costs, i.e., the costs for the defender of switching from a given strategy to another one at successive rounds of a Nash game. The resulting problems are nonconvex QP ones with linear constraints and turn out to be very challenging. We will show that the most recent approaches for the minimization of nonconvex QP functions over polytopes, including commercial solvers such as and , are unable to solve to optimality even test instances with $$n=50$$ n = 50 variables. For this reason, we propose to extend with them the current benchmark set of test instances for QP problems. We also present a spatial branch-and-bound approach for the solution of these problems, where a predominant role is played by an optimality-based domain reduction, with multiple solutions of LP problems at each node of the branch-and-bound tree. Of course, domain reductions are standard tools in spatial branch-and-bound approaches. However, our contribution lies in the observation that, from the computational point of view, a rather aggressive application of these tools appears to be the best way to tackle the proposed instances. Indeed, according to our experiments, while they make the computational cost per node high, this is largely compensated by the rather slow growth of the number of nodes in the branch-and-bound tree, so that the proposed approach strongly outperforms the existing solvers for QP problems.

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Section: Branchingmentioning

confidence: 99%

Section: } Respectively (Quaternary Branching); Branching On Xmentioning

confidence: 99%

Section: Example: Crime Prevention By Patrolling (Of the Police)mentioning

confidence: 99%

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Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems

et al. 2021

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“…GSGs [1,7] belong to the larger class of SSGs [12,20], which feature interactions between two players, a leader and a follower. The two players need not necessarily be individuals.…”

Section: Preliminaries 21 Green Security Gamesmentioning

confidence: 99%

“…We therefore introduce a unified approach for computing strategies for resource allocation and subsequent patrolling in GSGs while also taking into account uncertainty in real-time information, to develop strategic defender allocation and patrolling strategies with inter-resource communication and signaling. We list our contributions as follows: (1) We propose a game model with two stages that captures real-time information through signaling and communication within a team of players; the first stage for handling resource allocation and the second stage for patrolling once the allocation decision has been made. This will be an imperfectinformation Extensive Form Game (EFG) capable of representing real-world scenarios with multiple types of defender agents and multiple attackers.…”

Section: Introductionmentioning

confidence: 99%

Reinforcement Learning for Unified Allocation and Patrolling in Signaling Games with Uncertainty

Venugopal,

Bondi,

Kamarthi

et al. 2020

Preprint

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Green Security Games (GSGs) have been successfully used in the protection of valuable resources such as fisheries, forests and wildlife. While real-world deployment involves both resource allocation and subsequent coordinated patrolling with communication and realtime, uncertain information, previous game models do not fully address both of these stages simultaneously. Furthermore, adopting existing solution strategies is difficult since they do not scale well for larger, more complex variants of the game models.We therefore first propose a novel GSG model that combines defender allocation, patrolling, real-time drone notification to human patrollers, and drones sending warning signals to attackers. The model further incorporates uncertainty for real-time decisionmaking within a team of drones and human patrollers. Second, we present CombSGPO, a novel and scalable algorithm based on reinforcement learning, to compute a defender strategy for this game model. CombSGPO performs policy search over a multidimensional, discrete action space to compute an allocation strategy that is best suited to a best-response patrolling strategy for the defender, learnt by training a multi-agent Deep Q-Network. We show via experiments that CombSGPO converges to better strategies and is more scalable than comparable approaches. Third, we provide a detailed analysis of the coordination and signaling behavior learnt by CombSGPO, showing group formation between defender resources and patrolling formations based on signaling and notifications between resources. Importantly, we find that strategic signaling emerges in the final learnt strategy. Finally, we perform experiments to evaluate these strategies under different levels of uncertainty.

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