Mitigating the Curse of Correlation in Security Games by Entropy Maximization

In Stackelberg security games, a defender seeks to randomly allocate limited security resources to protect critical targets from an attack. In this paper, we study a fundamental, yet underexplored, phenomenon in security games, which we term the Curse of Correlation (CoC). Specifically, we observe that there are inevitable correlations among the protection status of different targets. Such correlation is a crucial concern, especially in spatio-temporal domains like conservation area patrolling, where attackers can surveil patrollers at certain areas and then infer their patrolling routes using such correlations. To mitigate this issue, we propose to design entropy-maximizing defending strategies for spatio-temporal security games, which frequently suffer from CoC. We prove that the problem is #P-hard in general. However, it admits efficient algorithms in well-motivated special settings.

[1]  Bo An,et al.  Deploying PAWS: Field Optimization of the Protection Assistant for Wildlife Security , 2016, AAAI.

[2]  Haifeng Xu,et al.  Security Games with Information Leakage: Modeling and Computation , 2015, IJCAI.

[3]  Steve Alpern,et al.  Patrolling Games , 2011, Oper. Res..

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

[5]  Bo An,et al.  Adversarial patrolling games , 2012, AAMAS.

[6]  Nicola Basilico,et al.  Leader-follower strategies for robotic patrolling in environments with arbitrary topologies , 2009, AAMAS.

[7]  Charles J. Colbourn,et al.  The complexity of computing the tutte polynomial on transversal matroids , 1995, Comb..

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

[9]  Branislav Bosanský,et al.  Comparing Strategic Secrecy and Stackelberg Commitment in Security Games , 2017, IJCAI.

[10]  Jeff Kahn,et al.  On the stochastic independence properties of hard-core distributions , 1997, Comb..

[11]  Vincent R. Nyirenda,et al.  Field foot patrol effectiveness in Kafue National Park, Zambia , 2012 .

[12]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[13]  Nicola Basilico,et al.  Patrolling security games: Definition and algorithms for solving large instances with single patroller and single intruder , 2012, Artif. Intell..

[14]  Branislav Bosanský,et al.  An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information , 2014, J. Artif. Intell. Res..

[15]  Juliane Hahn,et al.  Security And Game Theory Algorithms Deployed Systems Lessons Learned , 2016 .

[16]  Milind Tambe,et al.  Urban security: game-theoretic resource allocation in networked physical domains , 2010, AAAI 2010.

[17]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[18]  Branislav Bosanský,et al.  Combining Compact Representation and Incremental Generation in Large Games with Sequential Strategies , 2015, AAAI.

[19]  Branislav Bosanský,et al.  Computing time-dependent policies for patrolling games with mobile targets , 2011, AAMAS.

[20]  Haifeng Xu,et al.  Information Disclosure as a Means to Security , 2015, AAMAS.

[21]  Branislav Bosanský,et al.  Using Correlated Strategies for Computing Stackelberg Equilibria in Extensive-Form Games , 2016, AAAI.

[22]  William D. Moreto.  To conserve and protect: examining law enforcement ranger culture and operations in Queen Elizabeth National Park, Uganda , 2013 .

[23]  Vincent Conitzer,et al.  Computing optimal strategies to commit to in extensive-form games , 2010, EC '10.

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

[25]  Martin E. Dyer.  Approximate counting by dynamic programming , 2003, STOC '03.

[26]  Bo An,et al.  Computing Optimal Mixed Strategies for Security Games with Dynamic Payoffs , 2015, IJCAI.

[27]  Sarit Kraus,et al.  The impact of adversarial knowledge on adversarial planning in perimeter patrol , 2008, AAMAS.

[28]  Noga Alon,et al.  Adversarial Leakage in Games , 2013, SIAM J. Discret. Math..

[29]  Milind Tambe,et al.  Optimal patrol strategy for protecting moving targets with multiple mobile resources , 2013, AAMAS.

[30]  Branislav Bosanský,et al.  An Algorithm for Constructing and Solving Imperfect Recall Abstractions of Large Extensive-Form Games , 2017, IJCAI.

[31]  Martin E. Dyer,et al.  A polynomial-time algorithm to approximately count contingency tables when the number of rows is constant , 2002, STOC '02.

[32]  Ariel D. Procaccia,et al.  Learning Optimal Commitment to Overcome Insecurity , 2014, NIPS.

[33]  Milind Tambe,et al.  TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems , 2012, IAAI.

[34]  Mohit Singh,et al.  Entropy, optimization and counting , 2013, STOC.