# Diversified Multinomial Logit Contextual Bandits

arXiv: https://arxiv.org/abs/2607.11684 · HTML: https://mlsanity.com/paper/2607.11684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Combinatorial Multi-Armed Bandit with General Reward Functions](https://mlsanity.com/paper/1610.06603/) (2016)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Dynamic Assortment Optimization with Changing Contextual Information](https://mlsanity.com/paper/1810.13069/) (2018)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Contextual Combinatorial Bandits with Probabilistically Triggered Arms](https://mlsanity.com/paper/2303.17110/) (2023)
- [Combinatorial Neural Bandits](https://mlsanity.com/paper/2306.00242/) (2023)
- [Multinomial Logit Bandit with Linear Utility Functions](https://mlsanity.com/paper/1805.02971/) (2018)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [A Note on a Tight Lower Bound for MNL-Bandit Assortment Selection Models](https://mlsanity.com/paper/1709.06109/) (2017)
- [Contextual Multinomial Logit Bandits with General Value Functions](https://mlsanity.com/paper/2402.08126/) (2024)

## Abstract (arXiv)

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 textitdiversified 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 textitwhite-box UCB-based algorithm, textttOFU-DMNL, that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles. We show that textttOFU-DMNL achieves at least a (1-frac1e+1)-textitapproximate regret bound tildeOleft(d √T/Kright), 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 textttOFU-DMNL offers a statistically and computationally efficient solution.