Practical Scalability for Stackelberg Security Games

TL;DR

This paper introduces a unified model and approximation framework for Stackelberg Security Games, addressing scalability issues and providing solutions that significantly improve runtime efficiency with minimal quality loss.

Contribution

It presents a unified model called adversarial randomized allocation (ARA), establishes hardness results, and offers an approximation framework with practical scalability improvements.

Findings

Up to 1000x runtime improvement demonstrated

Acceptable 5% solution quality loss achieved

Hardness of approximation results for key sub-problems

Abstract

Stackelberg Security Games (SSGs) have been adopted widely for modeling adversarial interactions. With increasing size of the applications of SSGs, scalability of equilibrium computation is an important research problem. While prior research has made progress with regards to scalability, many real world problems cannot be solved satisfactorily yet as per current requirements; these include the deployed federal air marshals (FAMS) application and the threat screening (TSG) problem at airports. Further, these problem domains are inherently limited by NP hardness shown in prior literature. We initiate a principled study of approximations in zero-sum SSGs. Our contribution includes the following: (1) a unified model of SSGs called adversarial randomized allocation (ARA) games that allows studying most SSGs in one model, (2) hardness of approximation results for zero-sum ARA, as well as for the sub-problem of allocating federal air marshal (FAMS) and threat screening problem (TSG) at airports, (3) an approximation framework for zero-sum ARA with provable approximation guarantees and (4) experiments demonstrating the significant scalability of up to 1000x improvement in runtime with an acceptable 5% solution quality loss.