Contextual Multinomial Logit Bandits with General Value Functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914684726149120 |
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| author | Zhang, Mengxiao Luo, Haipeng |
| author_facet | Zhang, Mengxiao Luo, Haipeng |
| contents | Contextual multinomial logit (MNL) bandits capture many real-world assortment recommendation problems such as online retailing/advertising. However, prior work has only considered (generalized) linear value functions, which greatly limits its applicability. Motivated by this fact, in this work, we consider contextual MNL bandits with a general value function class that contains the ground truth, borrowing ideas from a recent trend of studies on contextual bandits. Specifically, we consider both the stochastic and the adversarial settings, and propose a suite of algorithms, each with different computation-regret trade-off. When applied to the linear case, our results not only are the first ones with no dependence on a certain problem-dependent constant that can be exponentially large, but also enjoy other advantages such as computational efficiency, dimension-free regret bounds, or the ability to handle completely adversarial contexts and rewards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contextual Multinomial Logit Bandits with General Value Functions Zhang, Mengxiao Luo, Haipeng Machine Learning Contextual multinomial logit (MNL) bandits capture many real-world assortment recommendation problems such as online retailing/advertising. However, prior work has only considered (generalized) linear value functions, which greatly limits its applicability. Motivated by this fact, in this work, we consider contextual MNL bandits with a general value function class that contains the ground truth, borrowing ideas from a recent trend of studies on contextual bandits. Specifically, we consider both the stochastic and the adversarial settings, and propose a suite of algorithms, each with different computation-regret trade-off. When applied to the linear case, our results not only are the first ones with no dependence on a certain problem-dependent constant that can be exponentially large, but also enjoy other advantages such as computational efficiency, dimension-free regret bounds, or the ability to handle completely adversarial contexts and rewards. |
| title | Contextual Multinomial Logit Bandits with General Value Functions |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.08126 |