  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 $\tilde O(\sqrt{n})$ regret. We
empirically test a scalable implementation of our algorithm and observe good
performance.
