On Using Admissible Bounds for Learning Forward Search Heuristics

Carlos Núñez-Molina, Masataro Asai, Juan Fernandez-Olivares, Pablo Mesejo

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: heuristic learning, neuro-symbolic AI, forward search, machine learning, automated planning, statistical modelling

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: We propose a method that leverages admissible heuristics as lower bounds of truncated gaussian distributions in order to improve heuristic learning in forward search.

Abstract:

In recent years, there has been growing interest in utilizing modern machine learning techniques to learn heuristic functions for forward search algorithms. Despite this, there has been little theoretical understanding of what they should learn, how to train them, and why we do so. This lack of understanding has resulted in the adoption of diverse training targets (suboptimal vs optimal costs vs admissible heuristics) and loss functions (e.g., square vs absolute errors) in the literature. In this work, we focus on how to effectively utilize the information provided by admissible heuristics in heuristic learning. We argue that learning from poly-time admissible heuristics by minimizing mean square errors (MSE) is not the correct approach, since its result is merely a noisy, inadmissible copy
of an efficiently computable heuristic. Instead, we propose to model the learned heuristic as a truncated gaussian, where admissible heuristics are used not as training targets but as lower bounds of this distribution. This results in a different loss function from the MSE commonly employed in the literature, which implicitly models the learned heuristic as a gaussian distribution. We conduct experiments where both MSE and our novel loss function are applied to learning a heuristic from optimal plan costs. Results show that our proposed method
converges faster during training and yields better heuristics, with 40% lower MSE on average.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 5741