[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86311-en":3,"doc-seo-86311-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86311,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","Diversified Multinomial Logit Contextual Bandits","Existing contextual multinomial logit (MNL) bandits capture relevance-driven choice but miss the potential gains from within-assortment diversity, while submodular/combinatorial bandits encode diversity in rewards but lack structured choice probabilities. A diversified multinomial logit (DMNL) contextual bandit integrates diversity into MNL choice probabilities via a generally submodular diversity function, formalizing the relevance–diversity trade-off within one model. Adding diversity makes exact MNL assortment optimization intractable, motivating the white-box OFU-DMNL algorithm for efficient exploration and computation.","arXiv :2607 . 11684v1 [ stat .ML] 13 Jul 2026  \nDiversified Multinomial Logit Contextual Bandits  \nHeesang Ann [sang3798@snu.ac.kr](sang3798@snu.ac.kr)  \nSeoul National University  \nTaehyun Hwang [th.hwang@snu.ac.kr](th.hwang@snu.ac.kr)  \nSeoul National University  \nMin-hwan Oh [minoh@snu.ac.kr](minoh@snu.ac.kr)  \nSeoul National University  \nAbstract  \nExisting contextual multinomial logit (MNL) bandits model relevance-driven choice but ignore the potential benefits of within-assortment diversity, while submodular/combinatorial bandits encode diversity in rewards but lack structured choice probabilities. We bridge this gap with the diversified multinomial logit (DMNL) contextual bandit, which augments MNL choice probabilities with a generally submodular diversity function, thereby formalizing the relevance–diversity trade-off within a single model. Incorporating diversity renders exact MNL assortment optimization intractable. We propose a white-box UCB-based algorithm, OFU-DMNL, that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles.  We show that OFU-DMNL achieves at least a (1 − e1 )-apasstpsaronoxrtmdaimerdatntseursibegzemro, etandubdlaorunTbdta􀀀dhoneprsiT/zoEKnx,p􀀁aeiwhdmerattenteasdindissetamhnoeincmstonpraterotexvtecddonimapsiepstnresonioxtinmg,Katainitoshnaefnmacd, axtoreirlmoatumveriveto exhaustive enumeration, comparable regret with substantially lower runtime. Overall, DMNL bandits provide a practical foundation for diversity-aware assortment optimization under uncertainty, and OFU-DMNL offers a statistically and computationally efficient solution.  \n1 Introduction  \nSequential assortment selection arises whenever a platform repeatedly presents a set of items and observes a user response. E-commerce websites curate product slates, streaming services recommend a set of movies, and app stores surface a collection of apps. In each round, the decision-making agent chooses an assortment subject to a size constraint, the user selectsat most one item (or makes no selection), and the agent updates future assortments based on the observed feedback. Because user preferences are not known a priori and must be learned from interactions with users, the problem is naturally cast as an online learning task: maximize cumulative reward while balancing exploration and exploitation.  \nA key ingredient in this setting is a probabilistic choice model that links an offered assortment to the user’s selection. The multinomial logit (MNL) model (McFadden et al. , 1978) has served as a canonical choice model for dynamic assortment learning: it represents choice probabilities through latent item utilities based on relevance, a structure that supports tractable assortment optimization and clean statistical learning guarantees. These advantages have motivated a substantial literature on MNL assortment bandits (Rusmevichientong et al. , 2010 ; Sauré and Zeevi, 2013 ; Agrawal et al. , 2017 ; 2019) and contextual variants that exploit user and item features to generalize across contexts (Cheung and Simchi-Levi, 2017 ; Ou  \nAnn, Hwang, and Oh  \net al. , 2018 ; Chen et al. , 2020 ; Oh and Iyengar, 2019 ; 2021 ; Perivier and Goyal, 2022 ; Zhang and Sugiyama, 2024 ; Lee and Oh, 2024 ; 2025) . In these models, uncertainty resides in the relevance-dependent utilities, and the agent’s task is to estimate them online efficiently enough to enable near-optimal sequential assortments.  \nHowever, practical assortment design is rarely driven by relevance alone: diversity within the offered set is often important in practice. Users tend to value assortments that span complementary attributes (e.g., different genres, brands, or styles), while assortments filled with near-duplicates can cannibalize one another and provide little additional benefit beyond offering a single representative item. At the same time, diversity is not a substitute for relevance: a diverse but irrelevant assortment still perform","cbCaipKpYrBefHVi","https://ap.wps.com/l/cbCaipKpYrBefHVi","pdf",29823217,5,1,39,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"How does DMNL differ from contextual multinomial logit (MNL) bandits?\",\"answer\":\"DMNL augments MNL choice probabilities with a submodular diversity function, explicitly modeling within-assortment diversity instead of relying only on relevance-driven utilities.\"},{\"question\":\"What challenge does diversity introduce into assortment optimization?\",\"answer\":\"With diversity incorporated, exact MNL assortment optimization becomes intractable, potentially requiring exhaustive search.\"},{\"question\":\"What is the key idea behind the OFU-DMNL algorithm?\",\"answer\":\"OFU-DMNL uses a white-box UCB-based approach that builds assortments item-wise by maximizing optimistic marginal gains, avoiding black-box optimization oracles 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does DMNL differ from contextual multinomial logit (MNL) bandits?","Question",{"text":76,"@type":77},"DMNL augments MNL choice probabilities with a submodular diversity function, explicitly modeling within-assortment diversity instead of relying only on relevance-driven utilities.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What challenge does diversity introduce into assortment optimization?",{"text":81,"@type":77},"With diversity incorporated, exact MNL assortment optimization becomes intractable, potentially requiring exhaustive search.",{"name":83,"@type":74,"acceptedAnswer":84},"What is the key idea behind the OFU-DMNL algorithm?",{"text":85,"@type":77},"OFU-DMNL uses a white-box UCB-based approach that builds assortments item-wise by maximizing optimistic marginal gains, avoiding black-box optimization oracles while improving runtime and maintaining regret 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