Learning More Expressive General Policies for Classical Planning Domains
This work addresses the problem of computational inefficiency in learning expressive general policies for AI planning, offering a more practical solution for researchers and practitioners in automated planning, though it is incremental in improving upon existing relational GNN architectures.
The paper tackles the limitation of GNN-based approaches for learning general policies in classical planning domains, which are confined to the expressive power of C2, by introducing a parameterized version R-GNN[t] that approximates more expressive 3-GNNs with reduced computational costs, achieving clear performance gains over existing methods like plain R-GNNs and Edge Transformers in experiments.
GNN-based approaches for learning general policies across planning domains are limited by the expressive power of $C_2$, namely; first-order logic with two variables and counting. This limitation can be overcame by transitioning to $k$-GNNs, for $k=3$, wherein object embeddings are substituted with triplet embeddings. Yet, while $3$-GNNs have the expressive power of $C_3$, unlike $1$- and $2$-GNNs that are confined to $C_2$, they require quartic time for message exchange and cubic space to store embeddings, rendering them infeasible in practice. In this work, we introduce a parameterized version R-GNN[$t$] (with parameter $t$) of Relational GNNs. Unlike GNNs, that are designed to perform computation on graphs, Relational GNNs are designed to do computation on relational structures. When $t=\infty$, R-GNN[$t$] approximates $3$-GNNs over graphs, but using only quadratic space for embeddings. For lower values of $t$, such as $t=1$ and $t=2$, R-GNN[$t$] achieves a weaker approximation by exchanging fewer messages, yet interestingly, often yield the expressivity required in several planning domains. Furthermore, the new R-GNN[$t$] architecture is the original R-GNN architecture with a suitable transformation applied to the inputs only. Experimental results illustrate the clear performance gains of R-GNN[$1$] over the plain R-GNNs, and also over Edge Transformers that also approximate $3$-GNNs.