arXiv:2504.21131v1 Announce Type: new 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.
The article “Dynamic Heuristics in Heuristic Search: A Framework for Optimality” explores the use of dynamic heuristics in heuristic search algorithms. While most heuristics used in these algorithms only depend on the current state, dynamic heuristics accumulate information during the search and also rely on the search history. The authors argue that existing approaches that incorporate dynamic heuristics in A*-like algorithms often overlook the complexities of searching with a mutable heuristic. In this paper, the authors formalize the concept of dynamic heuristics and propose a generic algorithm framework that incorporates them. They specifically examine an instantiation that models A* with dynamic heuristics and demonstrate general optimality results. Furthermore, the authors show how existing approaches in classical planning can be seen as special cases of this instantiation, allowing for the direct application of their optimality results.
Heuristic search algorithms have long been used to solve complex problems by guiding the search process with heuristics that estimate the cost of reaching the goal state. Traditionally, these heuristics relied solely on the current state being evaluated, providing a static estimation of the remaining cost. However, recent research has uncovered the potential benefits of dynamic heuristics that accumulate information during the search and depend on the search history.
In a new paper, titled “Dynamic Heuristics in Heuristic Search: A Novel Approach,” the authors explore the concept of dynamic heuristics and propose a generic algorithm framework that incorporates these heuristics. They specifically focus on modeling the well-known $mathrm{A}^*$ algorithm with dynamic heuristics and present general optimality results for this instantiation.
Understanding Dynamic Heuristics
Dynamic heuristics differ from their static counterparts in that they consider not only the current state being evaluated but also the search history. This additional information allows dynamic heuristics to adapt and refine their estimates as the search progresses. The authors argue that this adaptability can lead to improved performance and better solutions in many problem domains.
By formalizing the concept of dynamic heuristics, the authors provide a clear framework for incorporating them into existing search algorithms. This framework ensures that the benefits of dynamic heuristics can be achieved while also maintaining the theoretical foundations of the algorithm being used.
Optimality Results for Dynamic Heuristic $mathrm{A}^*$
To validate the effectiveness of dynamic heuristics, the authors apply their generic algorithm framework to the well-known $mathrm{A}^*$ algorithm. By integrating dynamic heuristics into $mathrm{A}^*$, they demonstrate that the algorithm can still guarantee optimality under certain conditions.
This result is significant because it shows that dynamic heuristics can be used in practice without sacrificing the theoretical guarantees that $mathrm{A}^*$ provides. By leveraging classic results for $mathrm{A}^*$, the authors are able to extend these guarantees to the dynamic heuristic variant of the algorithm.
Bridging the Gap with Classical Planning
An interesting aspect of the proposed framework is its ability to bridge the gap between heuristic search and classical planning. The authors demonstrate how existing approaches from classical planning can be viewed as special cases of the dynamic heuristic instantiation of $mathrm{A}^*$. This connection allows the optimality results obtained in their research to be directly applied to classical planning problems.
By applying dynamic heuristics to classical planning, researchers and practitioners in the field can benefit from the advantages offered by these heuristics. This opens up new possibilities for solving complex planning problems more efficiently and effectively.
Conclusion
The incorporation of dynamic heuristics into heuristic search algorithms brings new opportunities for solving complex problems. The generic algorithm framework proposed by the authors provides a solid foundation for integrating dynamic heuristics while preserving the theoretical guarantees of the underlying algorithm.
By applying this framework to $mathrm{A}^*$ with dynamic heuristics, the authors demonstrate that optimality can still be guaranteed under certain conditions. This research also establishes a connection between dynamic heuristics and classical planning, allowing for the direct application of their optimality results in planning problems.
As the field of heuristic search continues to evolve, the exploration of dynamic heuristics opens up new avenues for research and innovation. By embracing these new concepts and ideas, researchers and practitioners can push the boundaries of what is possible in solving complex problems.
The paper “Dynamic Heuristics in Heuristic Search” introduces the concept of dynamic heuristics in the context of heuristic search algorithms. While most heuristics used in heuristic search algorithms only depend on the current state, dynamic heuristics also take into account the search history and accumulate information during the search process. The authors argue that existing approaches that use dynamic heuristics in A*-like algorithms often rely on classic results for A* to prove optimality, but fail to consider the complexities that arise when using a mutable heuristic.
To address this issue, the authors propose a generic algorithm framework that formalizes the idea of dynamic heuristics. They also present a specific instantiation of this framework that models A* with dynamic heuristics and demonstrate general optimality results for this instantiation. By doing so, they aim to provide a better understanding of the complexities involved in searching with a mutable heuristic.
Moreover, the authors highlight that their framework can also be used to analyze existing approaches from classical planning, which can be viewed as special cases of their instantiation. This implies that the optimality results obtained in their study can be directly applied to these existing approaches, further enhancing their practical relevance.
Overall, this paper makes a valuable contribution to the field of heuristic search algorithms by formalizing the concept of dynamic heuristics and providing a framework for their analysis. The general optimality results presented in the paper have the potential to improve the performance and efficiency of heuristic search algorithms, particularly in domains where mutable heuristics are necessary.
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