Expressiveness of Graph Neural Networks in Planning Domains
Keywords: Classical Planning, Graph Neural Network, C2 Logic, Weisfeiler-Lehman algorithm
TL;DR: The paper investigates the limits of expressive power of graph neural networks in policy learning for PDDL domains.
Abstract: Graph Neural Networks (GNNs) have recently become the standard method of choice for learning with structured data, demonstrating particular promise in classical planning. Their inherent invariance under symmetries of the input graphs endows them with superior generalization capabilities compared to their symmetry-oblivious counterparts. However, this comes at the cost of limited expressive power. Notably, it is known that GNNs cannot distinguish between graphs that satisfy identical sentences of C$_2$ logic.
To leverage GNNs for learning policies in PDDL domains, one needs to encode the contextual representation of the planning states as graphs. The effectiveness of this encoding, coupled with a specific GNN architecture, hinges on the absence of indistinguishable states necessitating distinct actions. This paper provides a comprehensive theoretical and statistical exploration of such situations in PDDL domains across diverse natural encoding schemes and GNN models.
Primary Keywords: Learning
Category: Long
Student: No
Submission Number: 110
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