{"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/regret-in-online-combinatorial-optimization","title":"Regret in Online Combinatorial Optimization","arxiv_id":"1204.4710","date":"2012-04-20","proceeding":null,"authors":["Jean-Yves Audibert","Sébastien Bubeck","Gábor Lugosi"],"abstract":"We address online linear optimization problems when the possible actions of\nthe decision maker are represented by binary vectors. The regret of the\ndecision maker is the difference between her realized loss and the best loss\nshe would have achieved by picking, in hindsight, the best possible action. Our\ngoal is to understand the magnitude of the best possible (minimax) regret. We\nstudy the problem under three different assumptions for the feedback the\ndecision maker receives: full information, and the partial information models\nof the so-called \"semi-bandit\" and \"bandit\" problems. Combining the Mirror\nDescent algorithm and the INF (Implicitely Normalized Forecaster) strategy, we\nare able to prove optimal bounds for the semi-bandit case. We also recover the\noptimal bounds for the full information setting. In the bandit case we discuss\nexisting results in light of a new lower bound, and suggest a conjecture on the\noptimal regret in that case. Finally we also prove that the standard\nexponentially weighted average forecaster is provably suboptimal in the setting\nof online combinatorial optimization.","url_abs":"http://arxiv.org/abs/1204.4710v2","url_pdf":"http://arxiv.org/pdf/1204.4710v2.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":"regret-in-online-combinatorial-optimization","repo_url":"https://github.com/gitting-guud/GML_Project","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"combinatorial-optimization","task_name":"Combinatorial Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}