Oracle inequalities for computationally budgeted model selection

erieure Abstract We analyze general model selection procedures using penalized empirical loss minimiza- tion under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we argue that any practical model selection procedure must not only trade o estimation and approximation error, but also the eects of the computational eort required to compute empirical minimizers for dierent function classes. We provide a framework for analyzing such problems, and we give algorithms for model selection under a computational budget. These algorithms satisfy oracle inequalities that show that the risk of the selected model is not much worse than if we had devoted all of our computational budget to the best function class.