Differential Privacy in Personalized Pricing with Nonparametric Demand Models

52 Pages Posted: 10 Sep 2021 Last revised: 3 Aug 2022

See all articles by Xi Chen

Xi Chen

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

Sentao Miao

University of Colorado at Boulder

Yining Wang

University of Texas at Dallas

Date Written: September 8, 2021

Abstract

In the recent decades, the advance of information technology and abundant personal data facilitate the application of algorithmic personalized pricing. However, this leads to the growing concern of potential violation of privacy due to adversarial attack. To address the privacy issue, this paper studies a dynamic personalized pricing problem with \textit{unknown} nonparametric demand models under data privacy protection. Two concepts of data privacy, which have been widely applied in practices, are introduced: \textit{central differential privacy (CDP)} and \textit{local differential privacy (LDP)}, which is proved to be stronger than CDP in many cases. We develop two algorithms which make pricing decisions and learn the unknown demand on the fly, while satisfying the CDP and LDP gurantees respectively. In particular, for the algorithm with CDP guarantee, the regret is proved to be at most $\tilde O(T^{(d+2)/(d+4)}+\varepsilon^{-1}T^{d/(d+4)})$. Here, the parameter $T$ denotes the length of the time horizon, $d$ is the dimension of the personalized information vector, and the key parameter $\varepsilon>0$ measures the strength of privacy (smaller $\varepsilon$ indicates a stronger privacy protection). On the other hand, for the algorithm with LDP guarantee, its regret is proved to be at most $\tilde O(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$, which is near-optimal as we prove a lower bound of $\Omega(\varepsilon^{-2/(d+2)}T^{(d+1)/(d+2)})$ for any algorithm with LDP guarantee.

Keywords: Differential privacy, dynamic pricing, local privacy, regret

Suggested Citation

Chen, Xi and Miao, Sentao and Wang, Yining, Differential Privacy in Personalized Pricing with Nonparametric Demand Models (September 8, 2021). Available at SSRN: https://ssrn.com/abstract=3919807 or http://dx.doi.org/10.2139/ssrn.3919807

Xi Chen

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

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Sentao Miao

University of Colorado at Boulder ( email )

256 UCB
Boulder, CO CO 80300-0256
United States

Yining Wang (Contact Author)

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

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