## Dynamic pricing and assortment under a contextual MNL demand

### Noemie Perivier · Vineet Goyal

##### Hall J #836

Keywords: [ Online Learning ] [ assortment optimization ] [ multinomial logit ] [ contextual information ] [ dynamic pricing ]

[ Abstract ]
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Thu 1 Dec 9 a.m. PST — 11 a.m. PST

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 bound scales as $\tilde{O}(d\sqrt{\kappa T}+ \log(T)/\kappa)$, which gives a stronger bound than the existing $\tilde{O}(d\sqrt{T}/\kappa)$ guarantees.

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