Dynamic pricing and assortment under a contextual MNL demand
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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 κ (potentially exponentially small). Our regret upper bounds scale as Õ(d√(κ T)+ log(T)/κ), which gives a significantly stronger bound than the existing Õ(d√(T)/κ) guarantees.
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