Guarantees for Sound Abstractions for Generalized Planning (Extended Paper)

TL;DR

This paper develops a formal framework to analyze and guarantee the correctness of learned abstractions in generalized planning, enabling soundness assurances and invariant synthesis across collections of planning instances.

Contribution

It introduces a method to analyze and provide formal guarantees for inductively learned abstractions in generalized planning, enhancing their reliability and applicability.

Findings

Provides formal guarantees for abstraction correctness.

Enables definition of sound subcollections of instances.

Supports automated synthesis of planning invariants.

Abstract

Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to the planning problem for a qualitative numerical problem; the latter being a reformulation that simultaneously captures all the instances in the collection. An important thread of research thus consists in finding such reformulations, or abstractions, automatically. A recent proposal learns the abstractions inductively from a finite and small sample of transitions from instances in the collection. However, as in all inductive processes, the learned abstraction is not guaranteed to be correct for the whole collection. In this work we address this limitation by performing an analysis of the abstraction with respect to the collection, and show how to obtain formal guarantees for generalization. These guarantees, in the form of first-order formulas, may be used to 1) define subcollections of instances on which the abstraction is guaranteed to be sound, 2) obtain necessary conditions for generalization under certain assumptions, and 3) do automated synthesis of complex invariants for planning problems. Our framework is general, it can be extended or combined with other approaches, and it has applications that go beyond generalized planning.