Quality-bounded solutions for finite Bayesian Stackelberg games: scaling up

The fastest known algorithm for solving General Bayesian Stackelberg games with a finite set of follower (adversary) types have seen direct practical use at the LAX airport for over 3 years; and currently, an (albeit non-Bayesian) algorithm for solving these games is also being used for scheduling air marshals on limited sectors of international flights by the US Federal Air Marshals Service. These algorithms find optimal randomized security schedules to allocate limited security resources to protect targets. As we scale up to larger domains, including the full set of flights covered by the Federal Air Marshals, it is critical to develop newer algorithms that scale-up significantly beyond the limits of the current state-of-the-art of Bayesian Stackelberg solvers. In this paper, we present a novel technique based on a hierarchical decomposition and branch and bound search over the follower type space, which may be applied to different Stackelberg game solvers. We have applied this technique to different solvers, resulting in: (i) A new exact algorithm called HBGS that is orders of magnitude faster than the best known previous Bayesian solver for general Stackelberg games; (ii) A new exact algorithm called HBSA which extends the fastest known previous security game solver towards the Bayesian case; and (iii) Approximation versions of HBGS and HBSA that show significant improvements over these newer algorithms with only 1--2% sacrifice in the practical solution quality.

[1]  Bernhard von Stengel,et al.  Chapter 51 Inspection games , 2002 .

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

[3]  Murali S. Kodialam,et al.  Detecting network intrusions via sampling: a game theoretic approach , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[4]  Manish Jain,et al.  Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service , 2010, Interfaces.

[5]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[6]  Vincent Conitzer,et al.  Learning and Approximating the Optimal Strategy to Commit To , 2009, SAGT.

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

[8]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

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

[10]  Milind Tambe,et al.  Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks , 2011, AAMAS 2011.

[11]  G. Leitmann.  On generalized Stackelberg strategies , 1978 .

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

[13]  Milind Tambe,et al.  Approximation methods for infinite Bayesian Stackelberg games: modeling distributional payoff uncertainty , 2011, AAMAS.

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

[15]  R. Selten,et al.  A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information , 1972 .

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

[17]  Rudolf Avenhaus,et al.  Inspection Games , 2009, Encyclopedia of Complexity and Systems Science.

[18]  Michael P. Wellman,et al.  Approximate Strategic Reasoning through Hierarchical Reduction of Large Symmetric Games , 2005, AAAI.