Feature-Based Dynamic Pricing

Maxime C. Cohen (), Ilan Lobel () and Renato Paes Leme ()
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Maxime C. Cohen: Desaultels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada;
Ilan Lobel: NYU Stern School of Business, New York, New York 10012;
Renato Paes Leme: Google Research, New York, New York 10011

Management Science, 2020, vol. 66, issue 11, 4921-4943

Abstract: We consider the problem faced by a firm that receives highly differentiated products in an online fashion. The firm needs to price these products to sell them to its customer base. Products are described by vectors of features and the market value of each product is linear in the values of the features. The firm does not initially know the values of the different features, but can learn the values of the features based on whether products were sold at the posted prices in the past. This model is motivated by applications such as online marketplaces, online flash sales, and loan pricing. We first consider a multidimensional version of binary search over polyhedral sets and show that it has a worst-case regret which is exponential in the dimension of the feature space. We then propose a modification of the prior algorithm where uncertainty sets are replaced by their Löwner-John ellipsoids. We show that this algorithm has a worst-case regret which is quadratic in the dimension of the feature space and logarithmic in the time horizon. We also show how to adapt our algorithm to the case where valuations are noisy. Finally, we present computational experiments to illustrate the performance of our algorithm.

Keywords: online learning; contextual bandits; ellipsoid method; revenue management (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

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