论文标题
使用Gromov的链接条件来检测网格世界中的危险
Detecting danger in gridworlds using Gromov's Link Condition
论文作者
论文摘要
在AI研究中，尤其是在增强学习中，网格世界已经长期利用，因为它们为许多现实世界应用（例如机器人导航，新兴行为和操作研究）提供了简单而可扩展的模型。我们使用Abrams，Ghrist＆Peterson引起的可重构系统和州综合体的数学框架对网格世界进行了研究。状态络合物表示系统作为单个几何空间的所有可能配置，从而使它们有利于使用几何，拓扑或组合方法进行研究。这项工作的主要贡献是对原始的艾布拉姆斯，Ghrist和Peterson设置进行了修改，我们介绍这些设置以捕获代理编织，从而自然地代表了Gridworlds的拓扑。通过这种修改，状态络合物可能表现出几何缺陷（Gromov的链接条件的失败）。偶然地，我们发现这些故障完全发生在Gridworld中出现不良或危险状态的地方。因此，我们的结果提供了一种新颖的方法，可以在具有单个或多个代理的离散任务环境中寻求保证的安全限制，并提供有用的安全信息（以几何和拓扑形式）纳入或分析机器学习系统。从更广泛的角度来看，我们的工作从几何群体理论和组合学到AI社区介绍了工具，并通过简单的网格世界环境的示例来展示该任务域的几何观点的概念概念。
Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them conducive to study using geometric, topological, or combinatorial methods. The main contribution of this work is a modification to the original Abrams, Ghrist & Peterson setup which we introduce to capture agent braiding and thereby more naturally represent the topology of gridworlds. With this modification, the state complexes may exhibit geometric defects (failure of Gromov's Link Condition). Serendipitously, we discover these failures occur exactly where undesirable or dangerous states appear in the gridworld. Our results therefore provide a novel method for seeking guaranteed safety limitations in discrete task environments with single or multiple agents, and offer useful safety information (in geometric and topological forms) for incorporation in or analysis of machine learning systems. More broadly, our work introduces tools from geometric group theory and combinatorics to the AI community and demonstrates a proof-of-concept for this geometric viewpoint of the task domain through the example of simple gridworld environments.
