We study a discrete pricing setting where each customer is offered a contextual price. Often only historical sales records rather than customer valuations are available, where the data is influenced by the previous pricing policy. This introduces difficulties in estimating revenue. We approach this problem using ideas from learning with corrupted labels to formulate loss functions that directly optimize revenue, rather than going through an intermediate demand estimation stage.

Problem definition: This paper investigates the joint estimation of the consumer arrival rate and choice model parameters when ``no-purchasers” (customers who considered the product but did not purchase) are not observable. Estimating demand even with the simplest discrete-choice model such as the MNL becomes challenging as we do not know the fraction that have chosen the outside option (i.e., not purchased).

Mining for heterogeneous response to treatment is a crucial step in data-driven operations. We propose a partitioning algorithm to estimate heterogeneous odds ratio, a popular measure when response to treatment is binary. We integrate an adversarial imputation step to account for partially observed treatments (e.g., if full information is only available for purchased items). We validate our methodology on synthetic data and case studies from political science, medicine, and revenue management.