Transfer Learning for Nonparametric Contextual Dynamic Pricing

Fan Wang, Feiyu Jiang, Zifeng Zhao, Yi Yu

Abstract: Dynamic pricing strategies are crucial for firms to maximize revenue by adjusting prices based on market conditions and customer characteristics. However, designing optimal pricing strategies becomes challenging when historical data are limited, as is often the case when launching new products or entering new markets. One promising approach to overcome this limitation is to leverage information from related products or markets to inform the focal pricing decisions. In this paper, we explore transfer learning for nonparametric contextual dynamic pricing under a covariate shift model, where the marginal distributions of covariates differ between source and target domains while the reward functions remain the same. We propose a novel Transfer Learning for Dynamic Pricing (TLDP) algorithm that can effectively leverage pre-collected data from a source domain to enhance pricing decisions in the target domain. The regret upper bound of TLDP is established under a simple Lipschitz condition on the reward function. To establish the optimality of TLDP, we further derive a matching minimax lower bound, which includes the target-only scenario as a special case and is presented for the first time in the literature. Extensive numerical experiments validate our approach, demonstrating its superiority over existing methods and highlighting its practical utility in real-world applications.

Lay Summary:

Imagine you are running an online store and trying to set prices for your products based on customer characteristics to maximize your profit. This approach is known as contextual dynamic pricing. Now, imagine you’ve just launched your store in a new market. You don’t have much customer data yet, but you do have data from a similar market. Can this existing data help you make better pricing decisions in the new market, even if customer characteristics differ?

Our research introduces a new method that does exactly this. We develop an algorithm that transfers knowledge from a data-rich market (the source) to a new market (the target). Our method allows customer characteristics to vary across markets but assumes that the way these characteristics influence willingness to pay remains consistent. We provide theoretical guarantees showing that the proposed algorithm achieves optimal performance, and we demonstrate its effectiveness through both simulations and real-world data.

This work could help businesses make smarter pricing decisions more quickly in new markets by leveraging the data they already have, without having to wait months to collect new insights.

Link To Code: https://github.com/chrisfanwang/dynamic-pricing

Primary Area: Theory->Domain Adaptation and Transfer Learning

Keywords: Dynamic pricing, Transfer learning, Covariate shift, Minimax optimality

Submission Number: 4658