[Paper Review] Learning Domain-Independent Heuristics for Grounded and Lifted Planning

Dillon Z. Chen, Sylvie Thiébaux+1 more|arXiv (Cornell University)|Dec 18, 2023

AI-based Problem Solving and Planning4 citations

TL;DR

This paper introduces novel graph representations for planning tasks—grounded and lifted—that enable Graph Neural Networks (GNNs) to learn domain-independent heuristics without relying on grounded problem instances. The proposed GOOSE planner uses these representations to generalize to significantly larger problems than previous methods, outperforming STRIPS-HGN and $h^{\text{FF}}$ in plan quality and search efficiency on unseen tasks.

ABSTRACT

We present three novel graph representations of planning tasks suitable for learning domain-independent heuristics using Graph Neural Networks (GNNs) to guide search. In particular, to mitigate the issues caused by large grounded GNNs we present the first method for learning domain-independent heuristics with only the lifted representation of a planning task. We also provide a theoretical analysis of the expressiveness of our models, showing that some are more powerful than STRIPS-HGN, the only other existing model for learning domain-independent heuristics. Our experiments show that our heuristics generalise to much larger problems than those in the training set, vastly surpassing STRIPS-HGN heuristics.

Motivation & Objective

• To address the limitations of existing domain-independent heuristic learning models, such as STRIPS-HGN, which suffer from theoretical expressiveness issues and scalability problems.
• To develop new graph representations—grounded and lifted—for classical planning tasks that support effective GNN-based heuristic learning.
• To enable learning of domain-independent heuristics directly from lifted representations, avoiding the need for large grounded graphs.
• To theoretically analyze the expressive power of MPNNs on the proposed graphs in relation to known domain-independent heuristics.
• To empirically evaluate the performance of learned heuristics in heuristic search, measuring generalization, plan quality, and scalability.

Proposed method

• Propose three novel graph representations: Factual-Driven Representation (FDR), Grounded STRIPS (SLG), and Lifted STRIPS (LLG), to encode planning tasks for GNNs.
• Design a message-passing framework using MPNNs that operates on these graphs, with permutation-invariant aggregation functions to ensure generalization.
• Introduce a lifted graph representation that avoids grounding, enabling efficient learning on large-scale problems without constructing full grounded hypergraphs.
• Use mean and max pooling aggregators in GNNs to balance information retention and generalization, with ablation on hyperparameters like message-passing depth and aggregator choice.
• Implement the GOOSE planner, a heuristic search engine that uses GNN-learned heuristics and supports GPU-accelerated batch evaluation for high-speed state evaluation.
• Optimize GPU utilization by batching state evaluations, achieving sub-millisecond per-state inference times on lifted graphs with sufficient batch size.

Figure 5: (a) GOOSE learned heuristics ( $y$ -axis) vs. $h^{*}$ ( $x$ -axis). No $n$ -puzzle problem could have $h^{*}$ computed. (b) $h^{\operatorname*{FF}}$ ( $y$ -axis) vs. GOOSE ( $x$ -axis) on number of expanded nodes (left) and plan cost (right). Points on the bottom right triangles favour $h^

Experimental results

Research questions

• RQ1 Can graph representations of planning tasks be designed to support domain-independent heuristic learning via GNNs while avoiding the scalability issues of grounded representations?
• RQ2 Is it possible to learn effective domain-independent heuristics directly from lifted planning representations, without grounding?
• RQ3 How do the expressive powers of the proposed GNN models compare to STRIPS-HGN and known domain-independent heuristics?
• RQ4 To what extent do the learned heuristics generalize to problems larger than those in the training set?
• RQ5 How does the choice of graph representation and GNN hyperparameters (e.g., number of layers, aggregator type) affect heuristic accuracy and search performance?

Key findings

• The proposed GOOSE planner, using the SLG grounded graph with 8 layers and mean aggregator, generalizes to problems significantly larger than those in the training set, outperforming STRIPS-HGN and $h^{\text{FF}}$ in scalability and solution quality.
• Domain-independent GOOSE with the SLG graph outperforms $h^{\text{FF}}$ on VisitAll, VisitSome, and over half of Blocksworld instances, expanding fewer nodes and returning higher-quality plans.
• The lifted graph representation (LLG) enables domain-independent heuristic learning without grounding, making it feasible to handle large-scale problems that are intractable for grounded GNNs.
• GOOSE with domain-dependent training on the same graph representation achieves greater coverage than $h^{\text{FF}}$ in several domains and produces lower-cost plans.
• The optimal number of message-passing layers is 8–12 for domain-independent training and 4–8 for domain-dependent training; beyond this, performance degrades due to training instability and overfitting.
• GPU-accelerated evaluation reduces per-state heuristic inference time to 0.07–0.7ms for lifted graphs and 0.1–5ms for grounded graphs, with optimal performance at batch sizes >32 for lifted and >4 for grounded graphs.