# Dynamic pricing and assortment under a contextual MNL demand

arXiv: https://arxiv.org/abs/2110.10018 · HTML: https://mlsanity.com/paper/2110.10018/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Dynamic Assortment Optimization with Changing Contextual Information](https://mlsanity.com/paper/1810.13069/) (2018)
- [Multidimensional Binary Search for Contextual Decision-Making](https://mlsanity.com/paper/1611.00829/) (2016)
- [Online Stochastic Linear Optimization under One-bit Feedback](https://mlsanity.com/paper/1509.07728/) (2015)
- [Contextual Search via Intrinsic Volumes](https://mlsanity.com/paper/1804.03195/) (2018)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017)
- [Composite convex minimization involving self-concordant-like cost functions](https://mlsanity.com/paper/1502.01068/) (2015)
- [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019)

## Built on by (most cited first, 20 of 20)

- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [Model-Based Reinforcement Learning with Multinomial Logistic Function Approximation](https://mlsanity.com/paper/2212.13540/) (2022)
- [Provably Efficient Reinforcement Learning with Multinomial Logit Function Approximation](https://mlsanity.com/paper/2405.17061/) (2024)
- [Randomized Exploration for Reinforcement Learning with Multinomial Logistic Function Approximation](https://mlsanity.com/paper/2405.20165/) (2024)
- [Improved Algorithm for Adversarial Linear Mixture MDPs with Bandit Feedback and Unknown Transition](https://mlsanity.com/paper/2403.04568/) (2024)
- [Pricing with Contextual Elasticity and Heteroscedastic Valuation](https://mlsanity.com/paper/2312.15999/) (2023)
- [Contextual Multinomial Logit Bandits with General Value Functions](https://mlsanity.com/paper/2402.08126/) (2024)
- [Learning an Optimal Assortment Policy under Observational Data](https://mlsanity.com/paper/2502.06777/) (2025)
- [Enjoying Non-linearity in Multinomial Logistic Bandits: A Minimax-Optimal Algorithm](https://mlsanity.com/paper/2507.05306/) (2025)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [Dynamic Assortment Selection and Pricing with Censored Preference Feedback](https://mlsanity.com/paper/2504.02324/) (2025)
- [Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options](https://mlsanity.com/paper/2510.18713/) (2025)
- [On Pareto Optimality for Parametric Choice Bandits](https://mlsanity.com/paper/2501.19277/) (2025)
- [Stochastic Matching Bandits with Rare Optimization Updates](https://mlsanity.com/paper/2509.04194/) (2025)
- [Tractable Multinomial Logit Contextual Bandits with Non-Linear Utilities](https://mlsanity.com/paper/2601.06913/) (2026)
- [Minimax Optimal Variance-Aware Regret Bounds for Multinomial Logistic MDPs](https://mlsanity.com/paper/2605.19768/) (2026)
- [Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification](https://mlsanity.com/paper/2605.25592/) (2026)
- [Diversified Multinomial Logit Contextual Bandits](https://mlsanity.com/paper/2607.11684/) (2026)
- [Learning Choice Model Trees for Feature-Based Multi-Product Pricing: Exact Optimization and Field Evidence](https://mlsanity.com/paper/2609.16952/) (2026)

## Abstract (arXiv)

We consider dynamic multi-product pricing and assortment problems under an unknown demand over T periods, where in each period, the seller decides on the price for each product or the assortment of products to offer to a customer who chooses according to an unknown Multinomial Logit Model (MNL). Such problems arise in many applications, including online retail and advertising. We propose a randomized dynamic pricing policy based on a variant of the Online Newton Step algorithm (ONS) that achieves a O(d√Tlog(T)) regret guarantee under an adversarial arrival model. We also present a new optimistic algorithm for the adversarial MNL contextual bandits problem, which achieves a better dependency than the state-of-the-art algorithms in a problem-dependent constant kappa2 (potentially exponentially small). Our regret upper bound scales as tildeO(d√kappa2 T+ log(T)/kappa2), which gives a stronger bound than the existing tildeO(d√T/kappa2) guarantees.