  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.
