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Feature-Based Dynamic Pricing

39 Pages Posted: 29 Feb 2016 Last revised: 10 Dec 2016

Maxime C. Cohen

New York University (NYU) - Leonard N. Stern School of Business

Ilan Lobel

New York University (NYU)

Renato Paes Leme

Google Inc.

Date Written: February 23, 2016

Abstract

We consider the problem faced by a firm that receives highly differentiated products in an online fashion and needs to price them in order 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 it 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 a question in online advertising, where impressions arrive over time and can be described by vectors of features. We first consider a multi-dimensional version of binary search over polyhedral sets, and show that it has exponential worst-case regret. We then propose a modification of the prior algorithm where uncertainty sets are replaced by their Lowner-John ellipsoids. We show that this algorithm has a worst-case regret that is quadratic in the dimensionality 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 by using a technique called shallow cuts. Finally, we present computational experiments to illustrate the performance of our algorithm.

Keywords: Multi-armed bandits, contextual bandits, ellipsoid method, online advertising

JEL Classification: C61, D42, D81, D83

Suggested Citation

Cohen, Maxime C. and Lobel, Ilan and Paes Leme, Renato, Feature-Based Dynamic Pricing (February 23, 2016). Available at SSRN: https://ssrn.com/abstract=2737045

Maxime C. Cohen

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
New York, NY NY 10012
United States

Ilan Lobel (Contact Author)

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Renato Paes Leme

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

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