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Tree Search With Distributional Predictions
Data Structures and Algorithms · Submitted 26 Sep 2026
abstract compiled · 2026-09-29 · no language-model review
The authors' main claim We give an algorithm with expected query complexity $O\left(H(p)+k\log \eta \right)$, where $H(p)$ is the Shannon entropy of the true distribution and $\eta$ is the earth mover's distance between $p$ and $\widehat p$ in the tree metric.
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The abstract, sentence by sentence
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 $O\left(H(p)+k\log \eta \right)$, where $H(p)$ is the Shannon entropy of the true distribution and $\eta$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.06 | 0.06 | asserted 1.00 |
| s1 | We study this paradigm for search on trees. | contribution 0.76 | 0.51 | 0.02 | asserted 0.67 |
| s2 | 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 $t$. | background 0.95 | 0.08 | 0.02 | hedged possibility 0.73 |
| s3 | The goal is to find $t$ using as few queries as possible. | background 1.00 | 0.07 | 0.02 | asserted 0.97 |
| s4 | 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. | background 0.77 | 0.26 | 0.04 | asserted 0.92 |
| s5 | We give an algorithm with expected query complexity $O\left(H(p)+k\log \eta \right)$, where $H(p)$ is the Shannon entropy of the true distribution and $\eta$ is the earth mover's distance between $p$ and $\widehat p$ in the tree metric. | result 0.81 | 0.97 | 0.75 | asserted 1.00 |
| s6 | We also provide a matching lower bound that shows our algorithm is asymptotically tight. | result 0.85 | 0.95 | 0.21 | asserted 1.00 |
| s7 | 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. | result 0.99 | 0.96 | 0.29 | asserted 0.85 |
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Original abstract
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 $O\left(H(p)+k\log \eta \right)$, where $H(p)$ is the Shannon entropy of the true distribution and $\eta$ 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.
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