Memory Assignment for Finite-Memory Strategies in Adversarial Patrolling Games

TL;DR

This paper introduces a new iterative method for automatically assigning memory in finite-memory strategies for adversarial patrolling games, improving strategy construction without manual memory assignment.

Contribution

We develop a general algorithm that automatically optimizes memory assignment in finite-memory strategies, enhancing their practical usability in security game applications.

Findings

Our method effectively automates memory assignment in various patrolling models.

The algorithm is compatible with any black-box strategy optimization tool.

Experiments demonstrate robustness across different game instances.

Abstract

Adversarial Patrolling games form a subclass of Security games where a Defender moves between locations, guarding vulnerable targets. The main algorithmic problem is constructing a strategy for the Defender that minimizes the worst damage an Attacker can cause. We focus on the class of finite-memory (also known as regular) Defender's strategies that experimentally outperformed other competing classes. A finite-memory strategy can be seen as a positional strategy on a finite set of states. Each state consists of a pair of a location and a certain integer value--called memory. Existing algorithms improve the transitional probabilities between the states but require that the available memory size itself is assigned at each location manually. Choosing the right memory assignment is a well-known open and hard problem that hinders the usability of finite-memory strategies. We solve this issue by developing a general method that iteratively changes the memory assignment. Our algorithm can be used in connection with any black-box strategy optimization tool. We evaluate our method on various experiments and show its robustness by solving instances of various patrolling models.