# Contextual Multinomial Logit Bandits with General Value Functions

arXiv: https://arxiv.org/abs/2402.08126 · HTML: https://mlsanity.com/paper/2402.08126/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [The Statistical Complexity of Interactive Decision Making](https://mlsanity.com/paper/2112.13487/) (2021)
- [Taming the Monster: A Fast and Simple Algorithm for Contextual Bandits](https://mlsanity.com/paper/1402.0555/) (2014)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits under Realizability](https://mlsanity.com/paper/2003.12699/) (2020)
- [Feel-Good Thompson Sampling for Contextual Bandits and Reinforcement Learning](https://mlsanity.com/paper/2110.00871/) (2021)
- [Efficient First-Order Contextual Bandits: Prediction, Allocation, and Triangular Discrimination](https://mlsanity.com/paper/2107.02237/) (2021)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Fast rates in statistical and online learning](https://mlsanity.com/paper/1507.02592/) (2015)
- [Logistic Regression: The Importance of Being Improper](https://mlsanity.com/paper/1803.09349/) (2018)
- [Upper Counterfactual Confidence Bounds: a New Optimism Principle for Contextual Bandits](https://mlsanity.com/paper/2007.07876/) (2020)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [On the Complexity of Adversarial Decision Making](https://mlsanity.com/paper/2206.13063/) (2022)
- [Dynamic Assortment Optimization with Changing Contextual Information](https://mlsanity.com/paper/1810.13069/) (2018)
- [Fast Rates for General Unbounded Loss Functions: from ERM to Generalized Bayes](https://mlsanity.com/paper/1605.00252/) (2016)
- [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)
- [Contextual Bandits with Smooth Regret: Efficient Learning in Continuous Action Spaces](https://mlsanity.com/paper/2207.05849/) (2022)
- [Multinomial Logit Bandit with Linear Utility Functions](https://mlsanity.com/paper/1805.02971/) (2018)
- [A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit](https://mlsanity.com/paper/2011.14033/) (2020)
- [Adversarial Combinatorial Bandits with General Non-linear Reward Functions](https://mlsanity.com/paper/2101.01301/) (2021)
- [Practical Contextual Bandits with Feedback Graphs](https://mlsanity.com/paper/2302.08631/) (2023)
- [Multinomial Logit Bandit with Low Switching Cost](https://mlsanity.com/paper/2007.04876/) (2020)
- [Online Learning in Contextual Second-Price Pay-Per-Click Auctions](https://mlsanity.com/paper/2310.05047/) (2023)

## Built on by (most cited first, 4 of 4)

- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Near-Optimal Last-Iterate Convergence for Zero-Sum Games with Bandit Feedback and Opponent Actions](https://mlsanity.com/paper/2605.09363/) (2026)
- [Tractable Multinomial Logit Contextual Bandits with Non-Linear Utilities](https://mlsanity.com/paper/2601.06913/) (2026)
- [Diversified Multinomial Logit Contextual Bandits](https://mlsanity.com/paper/2607.11684/) (2026)

## Abstract (arXiv)

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.