Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Domain-Independent Heuristics for Grounded and Lifted Planning

Dillon Z. Chen, Sylvie Thiébaux, Felipe Trevizan

TL;DR

The experiments show that the heuristics generalise to much larger problems than those in the training set, vastly surpassing STRIPS-HGN heuristics.

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.

Learning Domain-Independent Heuristics for Grounded and Lifted Planning

TL;DR

The experiments show that the heuristics generalise to much larger problems than those in the training set, vastly surpassing STRIPS-HGN heuristics.

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.
Paper Structure (20 sections, 10 theorems, 9 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 10 theorems, 9 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Notation
  3. Planning
  4. Graph neural networks
  5. Representation
  6. Grounded Graphs
  7. Lifted Graphs
  8. Expressiveness
  9. Experiments
  10. GOOSE
  11. Setup
  12. Baselines
  13. Results
  14. How close to the optimal heuristic are our learned heurstics?
  15. How useful are learned domain-dependent heuristics for search?
  16. ...and 5 more sections

Key Result

Theorem 4.1

Let $L, B \in {\mathbb N}$, $\mathcal{G} \in \left\{ {SLG}, {FLG} \right\}$, $\varepsilon > 0$ and $h \in \{ h^{\mathop{\mathrm{add}}\limits}, h^{\max} \}$. Then there exists a set of parameters ${\Theta}$ for an MPNN ${\mathcal{F}}_{{\Theta}}$ such that for all planning tasks $\Pi$, if naive dynami

Figures (10)

  • Figure 1: The SLG subgraph of an action $a$ defined by $\mathop{\mathrm{pre}}\limits(a) = \left\{ p_0,p_1,p_2 \right\}$, $\mathop{\mathrm{add}}\limits(a) = \left\{ p_3,p_4 \right\}$ and $\mathop{\mathrm{del}}\limits(a) = \left\{ p_0,p_2 \right\}$, indicated by black, blue and red edges respectively.
  • Figure 2: The FLG subgraph of an action $a$ defined by $\mathop{\mathrm{pre}}\limits(a) = \left\{ \left< v_2,d_{2,1} \right>,\left< v_3,d_{3,2} \right> \right\}$ and $\mathop{\mathrm{eff}}\limits(a) = \{\left< v_1,d_{1,1} \right>$, $\left< v_2,d_{2,2} \right>$, $\left< v_3,d_{3,1} \right>\}$, indicated by black and blue edges respectively. Asparagus edges link variables and values.
  • Figure 3: LLG instance subgraph (a) and schema subgraph (b) with graph layer descriptions of a Blocksworld instance.
  • Figure 4: Expressiveness hierarchy of MPNNs on graph representations with respect to STRIPS-HGN and the heuristics $h^{\max}$, $h^{\mathop{\mathrm{add}}\limits}$, $h^+$ and $h^{*}$. Bold outlines represent new graphs.
  • Figure 5: (a) GOOSE learned heuristics ($y$-axis) vs. $h^{*}$ ($x$-axis). No $n$-puzzle problem could have $h^*$ computed. (b) $h^{\mathop{\mathrm{FF}}\limits}$ ($y$-axis) vs. GOOSE ($x$-axis) on number of expanded nodes (left) and plan cost (right). Points on the bottom right triangles favour $h^{\mathop{\mathrm{FF}}\limits}$ and on the top left triangles favour GOOSE. Problems unsolved by a configuration get value set to the maximum of the plot's axis.
  • ...and 5 more figures

Theorems & Definitions (18)

  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Theorem 4.1: MPNNs can learn $h^{\mathop{\mathrm{add}}\limits}$ and $h^{\max}$ on grounded graphs
  • Theorem 4.2: MPNNs on grounded graphs are strictly more expressive than STRIPS-HGN
  • Theorem 4.3: MPNNs cannot learn $h^{\mathop{\mathrm{add}}\limits}$ and $h^{\max}$ on lifted graphs
  • Theorem 4.4: MPNNs cannot learn $h^{+}$ or $h^{*}$ with our graphs
  • Theorem 4.5: MPNNs cannot learn any approximation of $h^{+}$ or $h^{*}$
  • Theorem A.1: MPNNs can learn $h^{\mathop{\mathrm{add}}\limits}$ and $h^{\max}$ on grounded graphs
  • proof
  • ...and 8 more