Minimizing Expected Intrusion Detection Time in Adversarial Patrolling

TL;DR

This paper introduces a new model for adversarial patrolling that focuses on minimizing the expected detection time of intrusions, providing optimal strategies and an efficient synthesis method.

Contribution

It formalizes a model where damage depends on detection time, proves the existence of optimal strategies, and develops a gradient-based algorithm for strategy synthesis.

Findings

Optimal strategies always exist for the new model.

Finite-memory strategies can approximate optimal protection.

An efficient gradient descent algorithm for strategy synthesis is proposed.

Abstract

In adversarial patrolling games, a mobile Defender strives to discover intrusions at vulnerable targets initiated by an Attacker. The Attacker's utility is traditionally defined as the probability of completing an attack, possibly weighted by target costs. However, in many real-world scenarios, the actual damage caused by the Attacker depends on the \emph{time} elapsed since the attack's initiation to its detection. We introduce a formal model for such scenarios, and we show that the Defender always has an \emph{optimal} strategy achieving maximal protection. We also prove that \emph{finite-memory} Defender's strategies are sufficient for achieving protection arbitrarily close to the optimum. Then, we design an efficient \emph{strategy synthesis} algorithm based on differentiable programming and gradient descent.