Scaling-up Security Games with Boundedly Rational Adversaries: A Cutting-plane Approach

To improve the current real-world deployments of Stackelberg security games (SSGs), it is critical now to efficiently incorporate models of adversary bounded rationality in large-scale SSGs. Unfortunately, previously proposed branch-and-price approaches fail to scale-up given the non-convexity of such models, as we show with a realization called COCOMO. Therefore, we next present a novel cutting-plane algorithm called BLADE to scale-up SSGs with complex adversary models, with three key novelties: (i) an efficient scalable separation oracle to generate deep cuts; (ii) a heuristic that uses gradient to further improve the cuts; (iii) techniques for quality-efficiency tradeoff.

[1]  Bo An,et al.  PROTECT: a deployed game theoretic system to protect the ports of the United States , 2012, AAMAS.

[2]  Sarit Kraus,et al.  Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition , 2010, Artif. Intell..

[3]  J. E. Kelley,et al.  The Cutting-Plane Method for Solving Convex Programs , 1960 .

[4]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[5]  L. Vandenberghe,et al.  Localization and Cutting-Plane Methods , 2007 .

[6]  Bo An,et al.  Mixed-Initiative Optimization in Security Games: A Preliminary Report , 2011, AAAI Spring Symposium: Help Me Help You: Bridging the Gaps in Human-Agent Collaboration.

[7]  Colin Camerer.  Behavioral Game Theory: Experiments in Strategic Interaction , 2003 .

[8]  Manish Jain,et al.  Computing optimal randomized resource allocations for massive security games , 2009, AAMAS.

[9]  Manish Jain,et al.  Security Games with Arbitrary Schedules: A Branch and Price Approach , 2010, AAAI.

[10]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[11]  Milind Tambe.  Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned , 2011 .

[12]  Vincent Conitzer,et al.  Complexity of Computing Optimal Stackelberg Strategies in Security Resource Allocation Games , 2010, AAAI.

[13]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[14]  Christos H. Papadimitriou.  Computing correlated equilibria in multi-player games , 2005, STOC '05.

[15]  Vincent Conitzer,et al.  Stackelberg vs. Nash in security games: interchangeability, equivalence, and uniqueness , 2010, AAMAS 2010.

[16]  T. Palfrey,et al.  Regular Quantal Response Equilibrium , 2005 .

[17]  Rong Yang,et al.  Computing optimal strategy against quantal response in security games , 2012, AAMAS.

[18]  Milind Tambe,et al.  The Deployment-to-Saturation Ratio in Security Games , 2012, AAAI.

[19]  Vincent Conitzer,et al.  Stackelberg vs. Nash in security games: interchangeability, equivalence, and uniqueness , 2010, AAMAS.

[20]  S. Vavasis.  COMPLEXITY ISSUES IN GLOBAL OPTIMIZATION: A SURVEY , 1995 .

[21]  Rong Yang,et al.  Improving Resource Allocation Strategy against Human Adversaries in Security Games , 2011, IJCAI.