R-GNN无法学习规划中的C₂特征，理论与实际表现不符。
Relational GNNs Cannot Learn $C_2$ Features for Planning
- 基于关系图神经网络的规划价值函数学习方法
- 实验证明其无法捕捉C₂逻辑特征，理论优势未实现
- 对规划领域图神经网络设计有重要警示意义
关系图神经网络（R-GNN）是一种基于GNN的学习方法，用于从给定规划领域中泛化到未见过的问题，并学习价值函数。R-GNN的理论基础源于图神经网络表达能力与C₂逻辑（一阶逻辑中含两个变量和计数的子集）之间的联系。在规划任务中，C₂特征指由规划领域的基数谓词和二元谓词构成的C₂公式集合。某些规划领域中，最优价值函数可表示为C₂特征的算术组合。本文证明，与先前的实验结果相反，R-GNN无法学习由C₂特征定义的价值函数。同时，我们识别出此前某些更适合学习此类特征的GNN架构。
原文摘要 · Abstract (English)
Relational Graph Neural Networks (R-GNNs) are a GNN-based approach for learning value functions that can generalise to unseen problems from a given planning domain. R-GNNs were theoretically motivated by the well known connection between the expressive power of GNNs and $C_2$, first-order logic with two variables and counting. In the context of planning, $C_2$ features refer to the set of formulae in $C_2$ with relations defined by the unary and binary predicates of a planning domain. Some planning domains exhibit optimal value functions that can be decomposed as arithmetic expressions of $C_2$ features. We show that, contrary to empirical results, R-GNNs cannot learn value functions defined by $C_2$ features. We also identify prior GNN architectures for planning that may better learn value functions defined by $C_2$ features.
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