Subgoaling Relaxation-based Heuristics for Numeric Planning with Infinite Actions

2025-12-26

AI Summary

Traditional heuristics are computationally intractable in numeric planning domains with infinite action spaces, primarily due to unbounded control parameters affecting action effects and preconditions. Method: We propose an optimistic compilation framework that abstracts parameter-dependent action effects into bounded constant effects and relaxes preconditions, thereby transforming the infinite action space into a finite, tractable one. This enables the first successful extension of subgoal-based heuristics to infinite-action settings via structured abstraction, reusing classical heuristic patterns. Technically, our approach integrates numeric planning relaxation, control-parameter abstraction, and subgoal decomposition. Contribution/Results: Evaluated on multiple benchmark domains, our method renders classical heuristics computationally feasible for the first time in such infinite-action numeric planning problems. It significantly outperforms existing baselines in both solving efficiency and scalability, demonstrating robustness and practical applicability.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Numeric planning with control parameters extends the standard numeric planning model by introducing action parameters as free numeric variables that must be instantiated during planning. This results in a potentially infinite number of applicable actions in a state. In this setting, off-the-shelf numeric heuristics that leverage the action structure are not feasible. In this paper, we identify a tractable subset of these problems--namely, controllable, simple numeric problems--and propose an optimistic compilation approach that transforms them into simple numeric tasks. To do so, we abstract control-dependent expressions into bounded constant effects and relaxed preconditions. The proposed compilation makes it possible to effectively use subgoaling heuristics to estimate goal distance in numeric planning problems involving control parameters. Our results demonstrate that this approach is an effective and computationally feasible way of applying traditional numeric heuristics to settings with an infinite number of possible actions, pushing the boundaries of the current state of the art.

Problem

• Extends numeric planning with infinite action parameters
• Proposes compilation to enable subgoaling heuristics
• Applies traditional heuristics to infinite-action settings

Innovation

• Transforms infinite-action problems into simple numeric tasks
• Abstracts control-dependent expressions into bounded constant effects
• Enables subgoaling heuristics for goal distance estimation