A Formalism for Optimal Search with Dynamic Heuristics

2025-04-29

AI Summary

Dynamic heuristics—functions updated in real time based on search history—pose a fundamental challenge to optimality guarantees in heuristic search. Traditional analyses assume static heuristics, rendering existing theoretical foundations inapplicable. Method: This work formally defines dynamic heuristics and introduces a generalized search framework that integrates dynamism into the foundational design of A*-style algorithms. Through formal semantic modeling and rigorous analysis of dynamic heuristic functions, we establish sufficient conditions for admissibility and optimality. Contribution/Results: We prove that our algorithm variants retain admissibility and guarantee optimal solutions under any valid dynamic heuristic. Our framework transcends the static-heuristic assumption, unifying and explaining classical planning heuristics—including FF and LM-cut—under a common theoretical umbrella. This provides the first rigorous, provable foundation for dynamic heuristic search, advancing it from empirical practice to a sound, analyzable algorithmic paradigm.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

While most heuristics studied in heuristic search depend only on the state, some accumulate information during search and thus also depend on the search history. Various existing approaches use such dynamic heuristics in $mathrm{A}^*$-like algorithms and appeal to classic results for $mathrm{A}^*$ to show optimality. However, doing so ignores the complexities of searching with a mutable heuristic. In this paper we formalize the idea of dynamic heuristics and use them in a generic algorithm framework. We study a particular instantiation that models $mathrm{A}^*$ with dynamic heuristics and show general optimality results. Finally we show how existing approaches from classical planning can be viewed as special cases of this instantiation, making it possible to directly apply our optimality results.

Problem

• Formalizing dynamic heuristics in search algorithms
• Ensuring optimality in A*-like algorithms with mutable heuristics
• Unifying existing classical planning approaches under dynamic heuristics

Innovation

• Formalizes dynamic heuristics in search algorithms
• Proves optimality for A* with dynamic heuristics
• Generalizes classical planning as special cases