{"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/sequential-experimental-design-for","title":"Sequential Experimental Design for Transductive Linear Bandits","arxiv_id":"1906.08399","date":"2019-06-20","proceeding":"NeurIPS 2019 12","authors":["Tanner Fiez","Lalit Jain","Kevin Jamieson","Lillian Ratliff"],"abstract":"In this paper we introduce the transductive linear bandit problem: given a set of measurement vectors $\\mathcal{X}\\subset \\mathbb{R}^d$, a set of items $\\mathcal{Z}\\subset \\mathbb{R}^d$, a fixed confidence $\\delta$, and an unknown vector $\\theta^{\\ast}\\in \\mathbb{R}^d$, the goal is to infer $\\text{argmax}_{z\\in \\mathcal{Z}} z^\\top\\theta^\\ast$ with probability $1-\\delta$ by making as few sequentially chosen noisy measurements of the form $x^\\top\\theta^{\\ast}$ as possible. When $\\mathcal{X}=\\mathcal{Z}$, this setting generalizes linear bandits, and when $\\mathcal{X}$ is the standard basis vectors and $\\mathcal{Z}\\subset \\{0,1\\}^d$, combinatorial bandits. Such a transductive setting naturally arises when the set of measurement vectors is limited due to factors such as availability or cost. As an example, in drug discovery the compounds and dosages $\\mathcal{X}$ a practitioner may be willing to evaluate in the lab in vitro due to cost or safety reasons may differ vastly from those compounds and dosages $\\mathcal{Z}$ that can be safely administered to patients in vivo. Alternatively, in recommender systems for books, the set of books $\\mathcal{X}$ a user is queried about may be restricted to well known best-sellers even though the goal might be to recommend more esoteric titles $\\mathcal{Z}$. In this paper, we provide instance-dependent lower bounds for the transductive setting, an algorithm that matches these up to logarithmic factors, and an evaluation. In particular, we provide the first non-asymptotic algorithm for linear bandits that nearly achieves the information theoretic lower bound.","url_abs":"https://arxiv.org/abs/1906.08399v1","url_pdf":"https://arxiv.org/pdf/1906.08399v1.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":"sequential-experimental-design-for","repo_url":"https://github.com/fiezt/Transductive-Linear-Bandit-Code","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"drug-discovery","task_name":"Drug Discovery"},{"task_slug":"experimental-design","task_name":"Experimental Design"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1906.08399","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}