Dynamic pricing and assortment under a contextual MNL demand

• URL: http://arxiv.org/abs/2110.10018v1
• Date: Tue, 19 Oct 2021 14:37:10 GMT
• Title: Dynamic pricing and assortment under a contextual MNL demand
• Authors: Vineet Goyal and Noemie Perivier
• Abstract summary: We consider dynamic multi-product pricing and assortment problems under an unknown demand over T periods. We propose a randomized dynamic pricing policy based on a variant of the Online Newton Step algorithm (ONS) We also present a new optimistic algorithm for the adversarial MNL contextual bandits problem.
• Score: 2.1320960069210475
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $O(d\sqrt{T}\log(T))$ 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 $\kappa$ (potentially exponentially small). Our regret upper bounds scale as $\tilde{O}(d\sqrt{\kappa T}+ \log(T)/\kappa)$, which gives a significantly stronger bound than the existing $\tilde{O}(d\sqrt{T}/\kappa)$ guarantees.

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