Jointly Learning Prices and Product Features

Product Design is an important problem in marketing research where a firm tries to learn what features of a product are more valuable to consumers. We study this problem from the viewpoint of online learning: a firm repeatedly interacts with a buyer by choosing a product configuration as well as a price and observing the buyer's purchasing decision. The goal of the firm is to maximize revenue throughout the course of $T$ rounds by learning the buyer's preferences. We study both the case of a set of discrete products and the case of a continuous set of allowable product features. In both cases we provide nearly tight upper and lower regret bounds.