Skip to Main Content
Probabilistic predictive models are often used in decision optimization applications. Optimal decision making in these applications critically depends on the performance of the predictive models, especially the accuracy of their probability estimates. In this paper, we propose a probabilistic model for revenue maximization and cost minimization across applications in which a decision making agent is faced with a group of possible customers and either offers a variable discount on a product or service or expends a variable cost to attract positive responses. The model is based directly on optimizing expected revenue and makes explicit the relationship between revenue and the customer's response behavior. We derive an expectation maximization (EM) procedure for learning the parameters of the model from historical data, prove that the model is asymptotically insensitive to selection bias in historical decisions, and demonstrate in a series of experiments the method's utility for optimizing financial aid decisions at an international institute of higher learning.