Diversified Multinomial Logit Contextual Bandits

2026-07-13

AI Summary

This work addresses the limitation of existing contextual multinomial logit (MNL) bandit models, which capture only correlation-driven selection while neglecting the benefits of combinatorial diversity, and submodular bandits, which model diversity but lack structured choice probabilities. To bridge this gap, the paper proposes the Diverse MNL (DMNL) model, which for the first time integrates a general submodular diversity function into the MNL framework, enabling a unified treatment of the trade-off between relevance and diversity. Building on this model, the authors design a white-box UCB algorithm, OFU-DMNL, that combines optimistic estimates of marginal gains with submodular optimization theory to achieve a $(1 - 1/(e+1))$-approximation regret bound of $\tilde{O}(d\sqrt{T/K})$. Experiments demonstrate that the method attains regret performance comparable to exhaustive search while significantly reducing runtime and outperforming standard submodular baselines.

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 $\textit{diversified multinomial logit}$ (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 $\textit{white-box}$ UCB-based algorithm, $\texttt{OFU-DMNL}$, that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles. We show that $\texttt{OFU-DMNL}$ achieves at least a $(1-\frac{1}{e+1})$-$\textit{approximate}$ regret bound $\tilde{O}\left(d \sqrt{T/K}\right)$, 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 $\texttt{OFU-DMNL}$ offers a statistically and computationally efficient solution.

Problem

• contextual bandits
• multinomial logit
• diversity
• assortment optimization
• submodularity

Innovation

• diversified multinomial logit
• contextual bandits
• submodular diversity
• white-box UCB algorithm
• assortment optimization