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Contextual Multinomial Logit Bandits with General Value Functions
Preprint   Open access

Contextual Multinomial Logit Bandits with General Value Functions

Mengxiao Zhang and Haipeng Luo
ArXiv.org
Cornell University
02/18/2024
DOI: 10.48550/arxiv.2402.08126
url
https://doi.org/10.48550/arxiv.2402.08126View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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.
Computer Science - Learning

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