Now, let F(z)= zP(Z1 z). This, togetherwithcompactnessofX and , implies A3.

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.

They suggest a new algorithm and prove that it achieves logarithmic regret. Quality: Overall the results in the paper seem technically correct, but I had some concerns about the model/assumptions/results: - it is unclear to me how restrictive the parametric assumption that the expected log of the valuation is linear in the covariates. Although authors claim that predictor variables can be arbitrarily transformed, the task of designing the appropriate transformation, ie. "feature engineering", is a non-trivial task itself. Additionally it is unclear how realistic/flexible the logarithm/exponential relationship is, as it imposes that the valuations are exponentially far in relationship to the weighted covariate distances.

The paper studies a variant of "contextual dynamic pricing", with a parametric model of buyer valuations and non-parametric "residual noise". The model is "rigged" in a specific way which allows for a strong positive result (and reviewers agree this is a feature, not a bug). Reviews are largely positive, but not without some caveats. As per one of the comments, relation to "bandits with side information" should be clarified.

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.

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. Papers published at the Neural Information Processing Systems Conference.