Learning General Policies for Classical Planning Domains: Getting Beyond C_2

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 overcomed 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 for embeddings, rendering them impractical. In this work, we introduce a parameterized version of relational GNNs. When t is infinity, R-GNN[t] approximates 3-GNNs 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 C_3 features 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 input states only. Experimental results illustrate the clear performance gains of R-GNN[1] and R-GNN[2] over plain R-GNNs, and also over edge transformers that also approximate 3-GNNs.