Gradient Boosting Machines (GBMs) are highly effective learners, capable of modeling complex relationships in data. However, this flexibility comes at a cost: GBMs can readily overfit the training data, capturing noise and leading to poor generalization on new, unseen examples. This chapter concentrates on methods specifically designed to combat this tendency within the boosting framework.

We will examine various regularization strategies applicable to GBMs. You'll learn how controlling the complexity of the individual decision trees (base learners) through constraints like maximum depth or minimum samples per leaf helps prevent overfitting. We will revisit shrinkage, or the learning rate ($\eta$), analyzing its role as an implicit regularizer. Furthermore, we'll cover subsampling techniques (row and feature sampling), often referred to as Stochastic Gradient Boosting, which introduce randomness to improve model robustness. We will also explore how adding explicit penalty terms, such as $L_1$ and $L_2$ norms, to the objective function can directly regularize the model, a technique prominently featured in XGBoost. Finally, we'll discuss practical strategies like early stopping using a validation set to determine the optimal number of boosting iterations.

By working through this chapter, you will gain a practical understanding of how to diagnose potential overfitting in gradient boosting models and apply appropriate regularization techniques to build models that perform reliably on unseen data.