Strategic Network Inspection with Location-Specific Detection Capabilities

2024-04-17

arXiv.org

AI Summary

This paper studies a zero-sum game for critical infrastructure protection, where a defender optimizes the placement of a limited number of imperfect detectors to minimize the expected number of undetected attacks, while an attacker seeks to maximize it. Addressing challenges including imperfect detection, large-scale networks, and computational intractability of Nash equilibrium computation, we propose a novel algorithm integrating column generation with multiplicative weights update (MWU), leveraging supermodular structure. Our key contributions include: (i) deriving the first closed-form solution for the unnormalized relative entropy projection, implementable in linear time; and (ii) establishing rigorous convergence guarantees to an approximate Nash equilibrium. Evaluated on real-world natural gas pipeline network data, the algorithm scales to networks with thousands of nodes, generates high-quality strategies in real time, and significantly outperforms existing baseline methods.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Adversarial Agents
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We consider a two-person network inspection game, in which a defender positions a limited number of detectors to detect multiple attacks caused by an attacker. We assume that detection is imperfect, and each detector location is associated with a probability of detecting attacks within its set of monitored network components. The objective of the defender (resp. attacker) is to minimize (resp. maximize) the expected number of undetected attacks. To compute Nash Equilibria (NE) for this large-scale zero-sum game, we formulate a linear program with a small number of constraints, which we solve via column generation. We provide an exact mixed-integer program for the pricing problem, which entails computing a defender's pure best response, and leverage its supermodular structure to derive two efficient approaches to obtain approximate NE with theoretical guarantees: A column generation and a multiplicative weights update (MWU) algorithm with approximate best responses. To address the computational challenges posed by combinatorial attacker strategies, each iteration of our MWU algorithm requires computing a projection under the unnormalized relative entropy. We provide a closed-form solution and a linear-time algorithm for the projection problem. Our computational results in real-world gas distribution networks illustrate the performance and scalability of our solution approaches.

Problem

• Developing resource coordination strategies for imperfect detection systems
• Computing Nash equilibria in large-scale zero-sum inspection games
• Addressing computational challenges in combinatorial security games

Innovation

• Column generation for Nash equilibrium computation
• Mixed-integer program with supermodular structure analysis
• Multiplicative weights update with closed-form projections