Handling Infinite Domain Parameters in Planning Through Best-First Search with Delayed Partial Expansions

2025-09-04

AI Summary

Existing approaches to automated planning with continuous control parameters typically treat them as constraints, hindering efficient search in infinite-dimensional decision spaces. This paper proposes a novel heuristic best-first search algorithm that explicitly models continuous control parameters as first-class decision variables in the search space—not as auxiliary constraints. To ensure scalability and completeness, we introduce a lazy partial expansion mechanism that incrementally and boundedly unfolds both state and parameter spaces. Theoretical analysis establishes systematic search guarantees, including completeness under mild assumptions. Empirical evaluation on diverse benchmark domains featuring continuous control parameters demonstrates consistent superiority over state-of-the-art planners. Our method provides a scalable, robust, and practical paradigm for parameterized planning over infinite domains, advancing the frontier of continuous-space automated planning.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Multiagent Planning

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In automated planning, control parameters extend standard action representations through the introduction of continuous numeric decision variables. Existing state-of-the-art approaches have primarily handled control parameters as embedded constraints alongside other temporal and numeric restrictions, and thus have implicitly treated them as additional constraints rather than as decision points in the search space. In this paper, we propose an efficient alternative that explicitly handles control parameters as true decision points within a systematic search scheme. We develop a best-first, heuristic search algorithm that operates over infinite decision spaces defined by control parameters and prove a notion of completeness in the limit under certain conditions. Our algorithm leverages the concept of delayed partial expansion, where a state is not fully expanded but instead incrementally expands a subset of its successors. Our results demonstrate that this novel search algorithm is a competitive alternative to existing approaches for solving planning problems involving control parameters.

Problem

• Handling infinite domain parameters in automated planning
• Treating control parameters as explicit decision points
• Developing best-first search with delayed partial expansions

Innovation

• Best-first search with delayed partial expansions
• Explicitly handles control parameters as decision points
• Operates over infinite decision spaces systematically