# Memory Assignment for Finite-Memory Strategies in Adversarial Patrolling Games

arXiv: https://arxiv.org/abs/2505.14137 · HTML: https://mlsanity.com/paper/2505.14137/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 6 of 6)

- [Learn to Intervene: An Adaptive Learning Policy for Restless Bandits in Application to Preventive Healthcare](https://mlsanity.com/paper/2105.07965/) (2021)
- [Deep Reinforcement Learning for Green Security Games with Real-Time Information](https://mlsanity.com/paper/1811.02483/) (2018)
- [Adversarial patrolling with spatially uncertain alarm signals](https://mlsanity.com/paper/1506.02850/) (2015)
- [Regstar: Efficient Strategy Synthesis for Adversarial Patrolling Games](https://mlsanity.com/paper/2108.08950/) (2021)
- [Minimizing Expected Intrusion Detection Time in Adversarial Patrolling](https://mlsanity.com/paper/2202.01095/) (2022)
- [On-the-fly Adaptation of Patrolling Strategies in Changing Environments](https://mlsanity.com/paper/2206.08096/) (2022)

## Abstract (arXiv)

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.