Generalized Planning with Positive and Negative Examples

TL;DR

This paper introduces negative examples into generalized planning, enabling validation and quantitative assessment of plans' generalization, and demonstrates that using negative examples accelerates plan synthesis.

Contribution

It extends generalized planning by defining negative examples and incorporating them into plan validation and synthesis, improving efficiency and evaluation.

Findings

Negative examples improve plan synthesis speed.

Quantitative metrics effectively assess plan generalization.

Incorporating negative examples enhances planning in multiple domains.

Abstract

Generalized planning aims at computing an algorithm-like structure (generalized plan) that solves a set of multiple planning instances. In this paper we define negative examples for generalized planning as planning instances that must not be solved by a generalized plan. With this regard the paper extends the notion of validation of a generalized plan as the problem of verifying that a given generalized plan solves the set of input positives instances while it fails to solve a given input set of negative examples. This notion of plan validation allows us to define quantitative metrics to asses the generalization capacity of generalized plans. The paper also shows how to incorporate this new notion of plan validation into a compilation for plan synthesis that takes both positive and negative instances as input. Experiments show that incorporating negative examples can accelerate plan synthesis in several domains and leverage quantitative metrics to evaluate the generalization capacity of the synthesized plans.