[Paper Review] Expressing and Exploiting the Common Subgoal Structure of Classical Planning Domains Using Sketches: Extended Version

Dominik Drexler, Jendrik Seipp+1 more|arXiv (Cornell University)|May 10, 2021

AI-based Problem Solving and Planning33 references4 citations

TL;DR

This paper introduces policy sketches—a compact, domain-general language for expressing and exploiting the common subgoal structure in classical planning domains. By integrating user-provided sketches into the SIW algorithm (forming $σ\text{IW}_R$), the approach enables provably polynomial-time solutions for planning problems that are intractable under standard SIW due to high goal width or non-serializable subgoals.

ABSTRACT

Width-based planning methods deal with conjunctive goals by decomposing problems into subproblems of low width. Algorithms like SIW thus fail when the goal is not easily serializable in this way or when some of the subproblems have a high width. In this work, we address these limitations by using a simple but powerful language for expressing finer problem decompositions introduced recently by Bonet and Geffner, called policy sketches. A policy sketch over a set of Boolean and numerical features is a set of sketch rules that express how the values of these features are supposed to change. Like general policies, policy sketches are domain general, but unlike policies, the changes captured by sketch rules do not need to be achieved in a single step. We show that many planning domains that cannot be solved by SIW are provably solvable in low polynomial time with the SIW_R algorithm, the version of SIW that employs user-provided policy sketches. Policy sketches are thus shown to be a powerful language for expressing domain-specific knowledge in a simple and compact way and a convenient alternative to languages such as HTNs or temporal logics. Furthermore, they make it easy to express general problem decompositions and prove key properties of them like their width and complexity.

Motivation & Objective

• Address the limitations of width-based planning methods like SIW, which struggle with non-serializable goals or high subproblem width.
• Provide a compact, interpretable, and domain-general language to express subgoal structures in planning domains without requiring PDDL-style action models.
• Enable polynomial-time solvability of benchmark planning problems previously intractable for pure width-based methods.
• Demonstrate that policy sketches serve as a practical alternative to HTNs and temporal logics for expressing general problem decompositions.
• Establish theoretical properties such as sketch width and complexity bounds for the resulting $σ\text{IW}_R$ algorithm.

Proposed method

• Use policy sketches—sets of rules $C \mapsto E$—to express how Boolean and numerical features should change across planning steps, without requiring single-step achievement.
• Define features $\Phi$ using counting, set operations, and distance functions over domain concepts (e.g., $\mathit{Count}(\mathit{locked}[0])$) to capture subgoal progress.
• Integrate sketches into the SIW algorithm to create $\sigma\text{IW}_R$, which uses sketch rules to guide subproblem decomposition and search.
• Construct sketches for benchmark domains (e.g., Grid, Childsnack, Driverlog, Schedule) using domain-specific concepts and roles to encode subgoal progress.
• Prove that the width of the sketch-defined subproblems is bounded, enabling polynomial-time execution of $\sigma\text{IW}_R$.
• Leverage the fact that sketch rules represent subgoals that can be achieved over multiple steps, allowing flexible and scalable decomposition.

Experimental results

Research questions

• RQ1 Can policy sketches express the subgoal structure of classical planning domains more effectively than traditional methods like HTNs or temporal logics?
• RQ2 Can the integration of user-provided sketches into SIW ($\sigma\text{IW}_R$) solve planning problems that are intractable under standard SIW due to high goal width?
• RQ3 What is the theoretical relationship between sketch width and the complexity of solving planning problems using $\sigma\text{IW}_R$?
• RQ4 How can sketches be constructed in a principled, domain-general way to ensure bounded width and polynomial-time solvability?
• RQ5 To what extent do sketches enable transparent, interpretable, and compact representation of domain-specific knowledge in planning?

Key findings

• Policy sketches allow the $\sigma\text{IW}_R$ algorithm to solve benchmark planning domains such as Grid, Childsnack, Driverlog, and Schedule in low polynomial time.
• Many planning problems that are infeasible for standard SIW due to high subproblem width or non-serializable goals become solvable via $\sigma\text{IW}_R$ when guided by appropriate sketches.
• The sketch width of the constructed sketches is bounded, which ensures that the $\sigma\text{IW}_R$ algorithm runs in polynomial time.
• Sketches provide a more transparent and compact alternative to HTNs and temporal logics for expressing general problem decompositions.
• The features used in sketches (e.g., $\mathit{Count}(\mathit{locked}[0])$, $\mathit{ConceptDist}(x_3,x_4,\mathit{truck}[0]\sqcap x_1[0])$) are expressive yet concise, enabling effective subgoal tracking.
• The approach enables planning with black-box simulators, as it does not require declarative PDDL-style action models, unlike hybrid width-based methods.