Optimization by gradient boosting
It provides theoretical foundations for gradient boosting, an incremental contribution to machine learning optimization methods.
The paper analyzes two widespread versions of gradient boosting, proving their convergence as iterations increase and highlighting the importance of a strongly convex risk functional, while also ensuring consistency as sample size grows without early stopping.
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization problem. We provide in the present paper a thorough analysis of two widespread versions of gradient boosting, and introduce a general framework for studying these algorithms from the point of view of functional optimization. We prove their convergence as the number of iterations tends to infinity and highlight the importance of having a strongly convex risk functional to minimize. We also present a reasonable statistical context ensuring consistency properties of the boosting predictors as the sample size grows. In our approach, the optimization procedures are run forever (that is, without resorting to an early stopping strategy), and statistical regularization is basically achieved via an appropriate $L^2$ penalization of the loss and strong convexity arguments.