{"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/statistically-efficient-polynomial-time","title":"Statistically Efficient, Polynomial Time Algorithms for Combinatorial Semi Bandits","arxiv_id":"2002.07258","date":"2020-02-17","proceeding":null,"authors":["Thibaut Cuvelier","Richard Combes","Eric Gourdin"],"abstract":"We consider combinatorial semi-bandits over a set of arms ${\\cal X} \\subset \\{0,1\\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\\cal O}\\Big( {d (\\ln m)^2 (\\ln T) \\over \\Delta_{\\min} }\\Big)$, but it has computational complexity ${\\cal O}(|{\\cal X}|)$ which is typically exponential in $d$, and cannot be used in large dimensions. We propose the first algorithm which is both computationally and statistically efficient for this problem with regret $R(T) = {\\cal O} \\Big({d (\\ln m)^2 (\\ln T)\\over \\Delta_{\\min} }\\Big)$ and computational complexity ${\\cal O}(T {\\bf poly}(d))$. Our approach involves carefully designing an approximate version of ESCB with the same regret guarantees, showing that this approximate algorithm can be implemented in time ${\\cal O}(T {\\bf poly}(d))$ by repeatedly maximizing a linear function over ${\\cal X}$ subject to a linear budget constraint, and showing how to solve this maximization problems efficiently.","url_abs":"https://arxiv.org/abs/2002.07258v2","url_pdf":"https://arxiv.org/pdf/2002.07258v2.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":"statistically-efficient-polynomial-time","repo_url":"https://github.com/dourouc05/CombinatorialBandits.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.07258","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}