Memory Assignment for Finite-Memory Strategies in Adversarial Patrolling Games
This work addresses a specific bottleneck in security games for defenders, making finite-memory strategies more usable, though it is incremental as it builds on existing optimization methods.
The paper tackles the problem of manually assigning memory sizes in finite-memory strategies for adversarial patrolling games, which is a known open and hard issue, by developing an iterative algorithm that automatically adjusts memory assignments and integrates with any black-box optimization tool, demonstrating robustness across various patrolling models in experiments.
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 \emph{any} black-box strategy optimization tool. We evaluate our method on various experiments and show its robustness by solving instances of various patrolling models.