{"id":505316,"date":"2018-09-10T18:58:43","date_gmt":"2018-09-11T01:58:43","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=505316"},"modified":"2018-10-16T20:21:28","modified_gmt":"2018-10-17T03:21:28","slug":"efficient-online-bandit-multiclass-learning-with-tildeosqrtt-regret","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/efficient-online-bandit-multiclass-learning-with-tildeosqrtt-regret\/","title":{"rendered":"Efficient Online Bandit Multiclass Learning with tilde{O}(sqrt{T}) Regret"},"content":{"rendered":"\n\n\n<p class=\"wp-block-paragraph\"><span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\">We present an efficient second-order algorithm with <\/span>\\(\\tilde{O}(\\frac{1}{\\eta\\sqrt{T}})\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\"> regret for the bandit online multiclass problem. The regret bound holds simultaneously with respect to a family of loss functions parameterized by <\/span>\\(\\eta\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\">, for a range of <\/span>\\(\\eta\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\"> restricted by the norm of the competitor. The family of loss functions ranges from hinge loss (<\/span>\\(\\eta =0\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\">) to squared hinge loss (<\/span>\\(\\eta =1\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\">). This provides a solution to the open problem of (J. Abernethy and A. Rakhlin. An efficient bandit algorithm for <\/span>\\(\\sqrt{\\sqrt{T}}\\)<span style=\"float: none;background-color: transparent;color: #000000;font-family: 'Lucida Grande',helvetica,arial,verdana,sans-serif;font-size: 14.4px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;line-height: 20px;text-align: left;text-decoration: none;text-indent: 0px\">-regret in online multiclass prediction? In COLT, 2009). We test our algorithm experimentally, showing that it also performs favorably against earlier algorithms. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present an efficient second-order algorithm with regret for the bandit online multiclass problem. The regret bound holds simultaneously with respect to a family of loss functions parameterized by , for a range of restricted by the norm of the competitor. The family of loss functions ranges from hinge loss () to squared hinge loss [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Alina Beygelzimer","user_id":0},{"type":"text","value":"Francesco Orabona","user_id":0},{"type":"user_nicename","value":"Chicheng Zhang","user_id":"36870"}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Conference on Machine Learning 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