We consider a canonical revenue maximization problem where customers arrive sequentially; each customer is interested in buying one product, and the customer purchases the product if her valuation for it exceeds the price set by the seller. The valuations of customers are not observed by the seller ; however, the seller can leverage contextual information available to her in the form of noisy covariate vectors describing the customer's history and the product's type to set prices. The seller can learn the relationship between covariates and customer valuations by experimenting with prices and observing transaction outcomes. We consider a semi-parametric model where the relationship between the expectation of the log of valuation and the covariates is linear (hence parametric) and the residual uncertainty distribution , i. e., the noise distribution , is non-parametric . We develop a pricing policy, DEEP-C, which learns this relationship with minimal exploration and in turn achieves optimal regretasymptotically in the time horizon\tilde  .
Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the residual uncertainty distribution . We develop a semi-parametric model in which the residual distribution is non-parametric and provide the first algorithm which learns both regression parameters and residual distribution with\tilde O(\sqrt{n .
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We consider a canonical revenue maximization problem where customers arrive sequentially; each customer is interested in buying one product, and the customer purchases the product if her valuation for it exceeds the price set by the seller. The valuations of customers are not observed by the seller ; however, the seller
Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller
D
available to her in the form of noisy covariate vectors
R
set prices. The seller can learn the relationship between covariates and customer valuations by experimenting with prices and observing transaction outcomes. We consider a semi-parametric model where the relationship between the expectation of the log of valuation and the covariates is linear (hence parametric) and the
predict her valuation of the product. However, her true valuation is unobservable to the seller, only binary outcome in the form of success-failure of a transaction is observed. Unlike in usual contextual bandit settings, the optimal price/arm given a covariate in our setting is sensitive to the detailed characteristics of the
R
, i. e., the noise distribution ,
. We develop a semi-parametric model in which the residual distribution
R
. We develop a pricing policy, DEEP-C, which learns this relationship with minimal exploration and in turn achieves optimal regretasymptotically in the time horizon
and provide the first algorithm which learns both regression parameters and residual distribution with
A
O(\sqrt{n