Machine learning with operational costs

This work concerns the way that statistical models are used to make decisions. In particular, we aim to merge the way estimation algorithms are designed with how they are used for a subsequent task. Our methodology considers the operational cost of carrying out a policy, based on a predictive model. The operational cost becomes a regularization term in the learning algorithm’s objective function, allowing either an optimistic or pessimistic view of possible costs. Limiting the operational cost reduces the hypothesis space for the predictive model, and can thus improve generalization. We show that different types of operational problems can lead to the same type of restriction on the hypothesis space, namely the restriction to an intersection of an ℓq ball with a halfspace. We bound the complexity of such hypothesis spaces by proposing a technique that involves counting integer points in polyhedrons.