A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint

53 Pages Posted: 2 Jan 2019

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Guillermo Gallego

Columbia University

Date Written: December 14, 2018

Abstract

A firm is selling a product to different types (based on the features such as education backgrounds, ages, etc.) of customers over a finite season with non-replenishable initial inventory. The type label of an arriving customer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.

Keywords: network revenue management, multi-armed bandit, learning and earning, dynamic pricing, online retailing

Suggested Citation

Chen, Ningyuan and Gallego, Guillermo, A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint (December 14, 2018). Available at SSRN: https://ssrn.com/abstract=3301153 or http://dx.doi.org/10.2139/ssrn.3301153

Ningyuan Chen (Contact Author)

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Guillermo Gallego

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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