{"id":823558,"date":"2022-03-02T09:32:34","date_gmt":"2022-03-02T17:32:34","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=823558"},"modified":"2022-03-02T09:32:34","modified_gmt":"2022-03-02T17:32:34","slug":"exploiting-correlation-to-achieve-faster-learning-rates-in-low-rank-preference-bandits","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/exploiting-correlation-to-achieve-faster-learning-rates-in-low-rank-preference-bandits\/","title":{"rendered":"Exploiting Correlation to Achieve Faster Learning Rates in Low-Rank Preference Bandits"},"content":{"rendered":"

We introduce the \\emph{Correlated Preference Bandits} problem with random utility-based choice models (RUMs), where the goal is to identify the best item from a given pool of\u00a0n<\/span><\/span><\/span><\/span> items through online subsetwise preference feedback. We investigate whether models with a simple correlation structure, e.g., low rank, can result in faster learning rates. While we show that the problem can be impossible to solve for the general `low rank’ choice models, faster learning rates can be attained assuming more structured item correlations. In particular, we introduce a new class of \\emph{Block-Rank} based RUM model, where the best item is shown to be\u00a0(<\/span>\u03f5<\/span>,<\/span>\u03b4<\/span>)<\/span><\/span><\/span><\/span>-PAC learnable with only\u00a0O<\/span>(<\/span>r<\/span>\u03f5<\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span>log<\/span><\/span>(<\/span>n<\/span>\/<\/span><\/span><\/span>\u03b4<\/span>)<\/span>)<\/span><\/span><\/span><\/span>\u00a0samples. This improves on the standard sample complexity bound of\u00a0O<\/span>~<\/span><\/span><\/span><\/span>(<\/span>n<\/span>\u03f5<\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span>log<\/span><\/span>(<\/span>1<\/span>\/<\/span><\/span><\/span>\u03b4<\/span>)<\/span>)<\/span><\/span><\/span><\/span>\u00a0known for the usual learning algorithms which might not exploit the item-correlations (r<\/span>\u226a<\/span>n<\/span><\/span><\/span><\/span>). We complement the above sample complexity with a matching lower bound (up to logarithmic factors), justifying the tightness of our analysis. Surprisingly, we also show a lower bound of\u00a0\u03a9<\/span>(<\/span>n<\/span>\u03f5<\/span>\u2212<\/span>2<\/span><\/span><\/span><\/span>log<\/span><\/span>(<\/span>1<\/span>\/<\/span><\/span><\/span>\u03b4<\/span>)<\/span>)<\/span><\/span><\/span><\/span>\u00a0when the learner is forced to play just duels instead of larger subsetwise queries. Further, we extend the results to a more general `\\emph{noisy Block-Rank}’ model, which ensures robustness of our techniques. Overall, our results justify the advantage of playing subsetwise queries over pairwise preferences\u00a0(<\/span>k<\/span>=<\/span>2<\/span>)<\/span><\/span><\/span><\/span>, we show the latter provably fails to exploit correlation.<\/p>\n","protected":false},"excerpt":{"rendered":"

We introduce the \\emph{Correlated Preference Bandits} problem with random utility-based choice models (RUMs), where the goal is to identify the best item from a given pool of\u00a0n items through online subsetwise preference feedback. We investigate whether models with a simple correlation structure, e.g., low rank, can result in faster learning rates. While we show that […]<\/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":null,"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":"AISTATS 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