Dynamic Pricing with Unknown Nonparametric Demand and Limited Price Changes

We consider the dynamic pricing problem of a retailer who does not have any information on the underlying demand for a product. The retailer aims to maximize cumulative revenue collected over a finite time horizon by balancing two objectives: learning demand and maximizing revenue. The retailer also seeks to reduce the amount of price experimentation because of the potential costs associated with price changes. Existing literature solves this problem in the case where the unknown demand is parametric. We consider the pricing problem when demand is nonparametric. We construct a pricing algorithm that uses second order approximations of the unknown demand function and establish when the proposed policy achieves near-optimal rate of regret, $\tilde{\mathcal{O}}(\sqrt{T})$, while making $\mathcal{O}(\log \log T)$ price changes. Hence, we show considerable reduction in price changes from the previously known $\mathcal{O}(\log T)$ rate of price change guarantee in the literature. We also perform extensive numerical experiments to show that the algorithm substantially improves over existing methods in terms of the total price changes, with comparable performance on the cumulative regret metric.

Funding: This work was supported by the National Science Foundation [Grant CMMI-156334].

Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2020.0445.