Dynamic pricing and assortment under a contextual MNL demand

2021/10/19 by Goyal, Vineet, Perivier, Noemie · 2 citations
#FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2110.10018

Abstract

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√(T)log(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 κ₂ (potentially exponentially small). Our regret upper bound scales as O(d√(κ₂ T)+ log(T)/κ₂), which gives a stronger bound than the existing O(d√(T)/κ₂) guarantees.

Cited by

• Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options
• Batched Stochastic Matching Bandits

Related

• MNL-Bandit with Knapsacks: a near-optimal algorithm
• Online Assortment and Price Optimization Under Contextual Choice Models
• A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit
• An Optimal Policy for Dynamic Assortment Planning Under Uncapacitated Multinomial Logit Models
• Dynamic Assortment Selection and Pricing with Censored Preference Feedback