Security Games with Arbitrary Schedules: A Branch and Price Approach

Abstract

Security games, and important class of Stackelberg games, are used in deployed decision-support tools in use by LAX police and the Federal Air Marshals Service. The algorithms used to solve these games find optimal randomized schedules to allocate security resources for infrastructure protection. Unfortunately, the state of the art algorithms either fail to scale or to provide a correct solution for large problems with arbitrary scheduling constraints. We introduce ASPEN, a branch-and-price approach that overcomes these limitations based on two key contributions: (i) A column-generation approach that exploits a novel network flow representation, avoiding a combinatorial explosion of schedule allocations; (ii) A branch-and-bound algorithm that generates bounds via a fast algorithm for solving security games with relaxed scheduling constraints. ASPEN is the first known method for efficiently solving massive security games with arbitrary schedules.

Artificial Intelligence for Social Impact: Learning and Planning in the Data‐to‐Deployment Pipeline

“…However, the defender's scheduling problem is considerably more challenging because each marshal's patrol must be a cycle. We were, once again, involved in the entire pipeline from immersion to deployment, which yielded the Intelligent Randomization in Scheduling system (Jain et al 2010a(Jain et al , 2010b. Intelligent Randomization in Scheduling was evaluated independently by the Transport Security Administration and found to be useful, and it is still in deployment today.…”

Playing Stackelberg Security Games in perfect formulations

“…We first compare our general methodology (using compact formulations and column generation) with branch-and-price on D2 (non-compact formulation) using the methodology of Jain et al [23]. We then run different tests using our approach, comparing different formulations and instances.…”

“…In a second stage, we obtain feasible strategies in the original space using a column generation approach where the pricing subproblem is polynomial (implementation phase). This twostage method outperforms the traditional branch-and-price based on the non-compact formulation D2 of Jain et al [23]. We use some problems already studied in the literature as examples: protecting targets with fairness constraints and combined resources.…”

Stackelberg Security Games: Models, Applications and Computational Aspects

“…Jain et al in [16] considered large, arbitrary schedules in the Stackelberg security game. The main idea of their model is to represent strategy space for defender using column generation, subcompositions into smaller problems, and a technique for searching the space of attacker strategies.…”