{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/binary-search-with-distributional-predictions","title":"Binary Search with Distributional Predictions","arxiv_id":"2411.16030","date":"2024-11-25","proceeding":null,"authors":["Michael Dinitz","Sungjin Im","Thomas Lavastida","Benjamin Moseley","Aidin Niaparast","Sergei Vassilvitskii"],"abstract":"Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \\log \\eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\\eta$ is the earth mover's distance between $p$ and the predicted distribution $\\hat p$. This also yields the first distributionally-robust algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.","url_abs":"https://arxiv.org/abs/2411.16030v1","url_pdf":"https://arxiv.org/pdf/2411.16030v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"binary-search-with-distributional-predictions","repo_url":"https://github.com/AidinNiaparast/Learned-BST","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"prediction","task_name":"Prediction"}],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2411.16030","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}