A Formalism for Optimal Search with Dynamic Heuristics (Extended Version)
This work addresses a theoretical gap in heuristic search for AI and planning, providing a formalism to ensure optimality in algorithms using dynamic heuristics, which is incremental as it builds on existing A*-like methods.
The paper tackles the problem of optimal search with dynamic heuristics, which depend on search history, by formalizing the concept and developing a generic algorithm framework. It shows general optimality results for an instantiation modeling A* with dynamic heuristics and demonstrates that existing approaches in classical planning are special cases, enabling direct application of these results.
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.