Diversified Multinomial Logit Contextual Bandits
Abstract
Existing 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 (1−1/(e+1))-approximate regret bound Õ(d √(T/K)), where d is the context dimension, K the maximum assortment size, and T the horizon, and attains an improved approximation factor over standard submodular baselines. Experiments demonstrate consistent gains and, relative to 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.
Related
- Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification
- Set Membership Estimation for Stochastic Linear Contextual Bandits
- Meta-LinEXP3: Online-within-Online Learning for Adversarial Linear Contextual Bandits
- Policy Regret for Embedding Model Routing: Contextual Bandits with Low-Rank Experts
- Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability
BibTeX
@misc{ann2026diversified,
title = {{Diversified Multinomial Logit Contextual Bandits}},
author = {Heesang Ann and Taehyun Hwang and Min-hwan Oh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.11684},
eprint = {2607.11684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11684},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Diversified Multinomial Logit Contextual Bandits
AU - Heesang Ann
AU - Taehyun Hwang
AU - Min-hwan Oh
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2607.11684
UR - https://arxiv.org/abs/2607.11684
AB - Existing 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 (1−1/(e+1))-approximate regret bound Õ(d √(T/K)), where d is the context dimension, K the maximum assortment size, and T the horizon, and attains an improved approximation factor over standard submodular baselines. Experiments demonstrate consistent gains and, relative to 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.
ER -