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Return to Tradition: Learning Reliable Heuristics with Classical Machine Learning

Dillon Z. Chen, Felipe Trevizan, Sylvie Thiébaux

TL;DR

This work constructs novel graph representations of lifted planning tasks and uses the WL algorithm to generate features from them, and develops WL-GOOSE, the first learning for planning model which reliably learns heuristics from scratch and outperforms the hFF heuristic in a fair competition setting.

Abstract

Current approaches for learning for planning have yet to achieve competitive performance against classical planners in several domains, and have poor overall performance. In this work, we construct novel graph representations of lifted planning tasks and use the WL algorithm to generate features from them. These features are used with classical machine learning methods which have up to 2 orders of magnitude fewer parameters and train up to 3 orders of magnitude faster than the state-of-the-art deep learning for planning models. Our novel approach, WL-GOOSE, reliably learns heuristics from scratch and outperforms the $h^{\text{FF}}$ heuristic in a fair competition setting. It also outperforms or ties with LAMA on 4 out of 10 domains on coverage and 7 out of 10 domains on plan quality. WL-GOOSE is the first learning for planning model which achieves these feats. Furthermore, we study the connections between our novel WL feature generation method, previous theoretically flavoured learning architectures, and Description Logic Features for planning.

Return to Tradition: Learning Reliable Heuristics with Classical Machine Learning

TL;DR

This work constructs novel graph representations of lifted planning tasks and uses the WL algorithm to generate features from them, and develops WL-GOOSE, the first learning for planning model which reliably learns heuristics from scratch and outperforms the hFF heuristic in a fair competition setting.

Abstract

Current approaches for learning for planning have yet to achieve competitive performance against classical planners in several domains, and have poor overall performance. In this work, we construct novel graph representations of lifted planning tasks and use the WL algorithm to generate features from them. These features are used with classical machine learning methods which have up to 2 orders of magnitude fewer parameters and train up to 3 orders of magnitude faster than the state-of-the-art deep learning for planning models. Our novel approach, WL-GOOSE, reliably learns heuristics from scratch and outperforms the heuristic in a fair competition setting. It also outperforms or ties with LAMA on 4 out of 10 domains on coverage and 7 out of 10 domains on plan quality. WL-GOOSE is the first learning for planning model which achieves these feats. Furthermore, we study the connections between our novel WL feature generation method, previous theoretically flavoured learning architectures, and Description Logic Features for planning.
Paper Structure (15 sections, 5 theorems, 7 equations, 8 figures, 6 tables, 1 algorithm)

This paper contains 15 sections, 5 theorems, 7 equations, 8 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Notation
  3. Planning
  4. The Weisfeiler-Leman algorithms
  5. WL Features for Planning
  6. Theoretical Results
  7. Experiments
  8. Conclusion
  9. Summary of Theoretical Results
  10. A.1. $\mathcal{WLF}^{\text{ILG}{}}$
  11. A.2. $\mathcal{GN\!N}^{\text{ILG}{}}$
  12. A.3. $\mathcal{DLF}$
  13. A.4. $\text{Muninn} = \mathcal{GN\!N}^{\text{MuG}}$
  14. More Detailed Evaluation Results
  15. Training Results

Key Result

Theorem 4.1

Let $\Pi_1$ and $\Pi_2$ be any two planning tasks from a given domain. If for a set of parameters $\mathbf{\Theta}$ we have that $\mathcal{GN\!N}^{\text{ILG}{}}_{\mathbf{\Theta}}(\Pi_1)\not=\mathcal{GN\!N}^{\text{ILG}{}}_{\mathbf{\Theta}}(\Pi_2)$, then there exists a corresponding set of parameters

Figures (8)

  • Figure 1: Two non-isomorphic graphs $G_1$ (6-cycle) and $G_2$ (two disjoint 3-cycles) which the WL algorithm returns the same outputs, thus failing to distinguishing them.
  • Figure 2: ILG subgraph of facts and goal condition corresponding to the $\emph{on}$ predicate of a Blocksworld instance. The current state says that $a$ stacked on $b$, which is stacked on $c$, and the goal condition is for $c$ to be stacked on $a$.
  • Figure 3: Expressivity hierarchy of WL, GNN and DL generated features for planning.
  • Figure 4: ILG and Muninn graph representations of tasks in Thm. \ref{['thm:gnn_muninn']} [$\supsetneq$].
  • Figure 5: ILG representations of tasks in Thm. \ref{['thm:wl_dl']} [$\exists$$<$].
  • ...and 3 more figures

Theorems & Definitions (9)

  • Definition 3.1
  • Theorem 4.1: $\mathcal{WLF}^{\text{ILG}{}}$ and $\mathcal{GN\!N}^{\text{ILG}{}}$ have the same power at distinguishing planning tasks.
  • proof : Proof
  • Theorem 4.2: $\mathcal{GN\!N}^{\text{ILG}{}}$ is strictly more expressive than $\text{Muninn}$ at distinguishing planning tasks.
  • proof : Proof
  • Corollary 4.3: $\mathcal{WLF}^{\text{ILG}{}}$ is strictly more expressive than $\text{Muninn}$ at distinguishing planning tasks.
  • Theorem 4.4: $\mathcal{WLF}^{\text{ILG}{}}$ and $\mathcal{DLF}$ are incomparable at distinguishing planning tasks.
  • proof : Proof
  • Corollary 4.5: All feature generation models thus far cannot generate features that allow us to learn $h^*$ for all domains.