AI 中文总结
本文首次对不一致启发式A*算法进行平滑分析，证明在轻微随机扰动下其期望时间复杂度为多项式级，弥合了理论与实践之间的差距。
AI 中文摘要
A*搜索是人工智能中的一种基础路径查找算法。虽然可采纳且一致的启发式函数通过每个状态最多扩展一次来保证高效性能，但现代搜索应用经常使用从机器学习、随机评估等中得到的强大但不一致的启发式函数。使用这些不一致启发式函数的一个长期存在的理论障碍是灾难性节点重新扩展的风险，这会产生最坏情况下指数级的时间复杂度 $\Omega(2^n)$。然而，经验观察与这一悲观界限相矛盾，表明不一致的A*在实践中运行得非常高效。为了弥合理论与实际之间的这一显著差距，本文首次对使用不一致启发式函数的A*算法进行了平滑分析。我们通过对最坏情况搜索图的边权重施加轻微的随机扰动来模拟典型的现实世界噪声。我们的主要结果证明，不一致A*的期望平滑时间复杂度以多项式为界，具体地，总迭代次数为 $O(n^2 m \kappa)$，其中 $n$ 是节点数，$m$ 是边数，$\kappa$ 控制随机扰动的规模。此外，我们还表明，这一结果自然扩展到负权重图上Dijkstra算法的功能等价问题。
英文摘要
The A* search is a fundamental path-finding algorithm in artificial intelligence. While admissible and consistent heuristics guarantee efficient performance by expanding each state at most once, modern search applications frequently employ powerful but inconsistent heuristics derived from machine learning, randomized evaluations, etc. A long-standing theoretical barrier to using these inconsistent heuristics is the risk of catastrophic node re-expansion, which yields a worst-case exponential time complexity of $Ω(2^n)$. However, empirical observations contradict this pessimistic bound, demonstrating that inconsistent A* operates highly efficiently in practice. To bridge this significant gap between theory and practice, this paper presents the first smoothed analysis of the A* algorithm using inconsistent heuristics. We model typical real-world noise by applying slight random perturbations to the edge weights of worst-case search graphs. Our main result proves that the expected smoothed time complexity of inconsistent A* is bounded by a polynomial, specifically a total iteration number of $O(n^2 m κ)$, where $n$ is the number of nodes, $m$ is the number of edges, and $κ$ controls the scale of random perturbations. Furthermore, we also show that this result naturally extends to the functionally equivalent problem of Dijkstra's algorithm on negative-weight graphs.
