Distribution-free Contextual Dynamic Pricing

TL;DR

This paper introduces a distribution-free contextual dynamic pricing method that learns customer valuation functions and market noise simultaneously, achieving sub-linear regret bounds without prior noise distribution knowledge.

Contribution

It proposes a novel perturbed linear bandit framework with a modified upper confidence bound algorithm for distribution-free pricing under unknown noise.

Findings

The method achieves sub-linear regret bounds.

It outperforms existing models with known noise distributions.

Validated on simulations and real auto-loan data.

Abstract

Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer's valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer's true valuation, but instead needs to learn the valuation by leveraging contextual information and historical binary purchase feedbacks. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, where a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sub-linear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto-loan dataset.