Convex Optimization
Leader-follower strategies for robotic patrolling in environments with arbitrary topologies
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
GUARDS: game theoretic security allocation on a national scale
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Journal of Artificial Intelligence Research
Improving resource allocation strategy against human adversaries in security games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
PROTECT: a deployed game theoretic system to protect the ports of the United States
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
PROTECT: a deployed game theoretic system to protect the ports of the United States
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Game-theoretic randomization for security patrolling with dynamic execution uncertainty
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Scaling-up security games with boundedly rational adversaries: a cutting-plane approach
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
An extended study on multi-objective security games
Autonomous Agents and Multi-Agent Systems
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To step beyond the first-generation deployments of attacker-defender security games -- for LAX Police, US FAMS and others -- it is critical that we relax the assumption of perfect rationality of the human adversary. Indeed, this assumption is a well-accepted limitation of classical game theory and modeling human adversaries' bounded rationality is critical. To this end, quantal response (QR) has provided very promising results to model human bounded rationality. However, in computing optimal defender strategies in real-world security games against a QR model of attackers, we face difficulties including (1) solving a nonlinear non-convex optimization problem efficiently for massive real-world security games; and (2) addressing constraints on assigning security resources, which adds to the complexity of computing the optimal defender strategy. This paper presents two new algorithms to address these difficulties: Gosaq can compute the globally optimal defender strategy against a QR model of attackers when there are no resource constraints and gives an efficient heuristic otherwise; Pasaq in turn provides an efficient approximation of the optimal defender strategy with or without resource constraints. These two novel algorithms are based on three key ideas: (i) use of a binary search method to solve the fractional optimization problem efficiently, (ii) construction of a convex optimization problem through a non-linear transformation, (iii) building a piecewise linear approximation of the non-linear terms in the problem. Additional contributions of this paper include proofs of approximation bounds, detailed experimental results showing the advantages of Gosaq and Pasaq in solution quality over the benchmark algorithm (Brqr) and the efficiency of Pasaq. Given these results, Pasaq is at the heart of the PROTECT system, which is deployed for the US Coast Guard in the port of Boston, and is now headed to other ports.