Hierarchical Decomposition and Analysis for Generalized Planning

TL;DR

This paper introduces a novel framework for analyzing and evaluating generalized plans in AI, enabling better assessment of their scope, utility, and termination properties to facilitate their synthesis and learning.

Contribution

It develops a new conceptual framework with proof techniques and algorithms for hierarchical analysis of generalized plans, extending automatic assessment capabilities.

Findings

The methods can determine plan termination and goal reachability.

The approach extends the class of generalized plans that can be automatically assessed.

Empirical results demonstrate the effectiveness of the framework.

Abstract

This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains challenging due to fundamental gaps in methods for analyzing the scope and utility of a given generalized plan. This paper addresses these gaps by developing a new conceptual framework along with proof techniques and algorithmic processes for assessing termination and goal-reachability related properties of generalized plans. We build upon classic results from graph theory to decompose generalized plans into smaller components that are then used to derive hierarchical termination arguments. These methods can be used to determine the utility of a given generalized plan, as well as to guide the synthesis and learning processes for generalized plans. We present theoretical as well as empirical results illustrating the scope of this new approach. Our analysis shows that this approach significantly extends the class of generalized plans that can be assessed automatically, thereby reducing barriers in the synthesis and learning of reliable generalized plans.