Learning More Expressive General Policies for Classical Planning Domains

2024-03-18

AI Summary

This work addresses the expressive power bottleneck of universal policy learning in classical planning. Standard graph neural networks (GNNs) are limited to C₂-logic expressivity, while 3-GNNs achieve C₃ expressivity at prohibitive computational and memory cost. We propose the parametric relational GNN, R-GNN[t], the first GNN variant to progressively approximate C₃ expressivity via input-side tunable transformations—without architectural redesign. The hyperparameter *t* enables flexible trade-offs between expressivity and efficiency, maintaining only quadratic space complexity *O(n²)*. Our theoretical analysis integrates the *k*-GNN framework with first-order logic expressibility, enhanced by optimized message passing and embedding compression. Experiments on multiple planning benchmarks show that R-GNN[1] significantly outperforms standard R-GNN and Edge Transformer: it reduces training memory to *O(n²)*, accelerates inference, and achieves higher policy generalization accuracy.

Technology Category

• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Enhancing GNNs for planning domains
• Reducing computational complexity in R-GNNs
• Improving expressivity with parameterized R-GNNs

Innovation

• Transition to $k$-GNNs for $k=3$
• Introduce parameterized R-GNN[$t$]
• Use quadratic space for embeddings