发表机构
Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对树上搜索问题，提出一种利用分布预测的学习增强算法，其期望查询复杂度为 O(H(p)+k log η)，并证明渐近最优，实验显示比完全信任预测的基线更高效。
AI 中文摘要
学习增强算法利用机器学习预测来改进经典算法在预测准确时的保证，同时在预测不准确时仍保持严格的性能保证。我们针对树上的搜索问题研究这一范式。给定一棵包含未知目标顶点 $t$ 的树 $T$，算法可以查询任意顶点 $v$，并获知 $v$ 的哪个邻居位于从 $v$ 到 $t$ 的唯一路径上。目标是用尽可能少的查询找到 $t$。我们考虑分布设置，其中目标从未知分布 $p$ 中抽取，算法获得一个质量未知的预测分布 $\widehat p$。我们给出一个期望查询复杂度为 $O\left(H(p)+k\log \eta \right)$ 的算法，其中 $H(p)$ 是真实分布的香农熵，$\eta$ 是 $p$ 与 $\widehat p$ 在树度量下的推土机距离。我们还提供了一个匹配的下界，表明我们的算法是渐近紧的。最后，在真实世界和合成树上的实验表明，我们基于预测的算法比完全信任预测的简单基线使用更少的查询。
英文摘要
Learning-augmented algorithms use machine-learned predictions to improve classical algorithmic guarantees when the predictions are accurate, while retaining rigorous performance guarantees when they are not. We study this paradigm for search on trees. Given a tree $T$ containing an unknown target vertex $t$, an algorithm may query any vertex $v$ and learn which neighbor of $v$ lies on the unique path from $v$ to $t$. The goal is to find $t$ using as few queries as possible. We consider the distributional setting, in which the target is drawn from an unknown distribution $p$ and the algorithm is given a predicted distribution $\widehat p$ of unknown quality. We give an algorithm with expected query complexity $O\left(H(p)+k\log η\right)$, where $H(p)$ is the Shannon entropy of the true distribution and $η$ is the earth mover's distance between $p$ and $\widehat p$ in the tree metric. We also provide a matching lower bound that shows our algorithm is asymptotically tight. Finally, experiments on real-world and synthetic trees show that our prediction-based algorithm can use substantially fewer queries than a simple baseline that trusts the prediction completely.
