Gradient boosting for convex cone predict and optimize problems

Recently there has been a growing body of research on decision-aware predictive modelling (see for example [5, 4, 15, 16, 18, 21, 25]). A traditional'predict, then optimize' framework treats the prediction estimation and decision optimization problem independently. As such, an'objective mismatch' [20] can occur whereby improved prediction accuracy does not result in improved decision accuracy. Conversely, the smart'predict, then optimize' (SPO) [15] framework optimizes prediction models in order to minimize the final downstream decision regret. To date, the SPO framework has been studied in a general setting for linear and decision tree regression models [15, 16]. In this paper we present dboost, a general purpose framework that combines the strength of gradient boosting with the SPO framework. Previous work [19] considers gradient boosting for integrated prediction and optimization problems but only considers a small subset of optimization problems with linear inequality constraints.