Gradient Boosting builds models sequentially, where each new base learner, typically a decision tree, attempts to correct the errors made by the ensemble of preceding learners. This iterative refinement process, focused on the pseudo-residuals or gradients of the loss function with respect to the current predictions, is what gives gradient boosting its predictive strength. However, this very mechanism makes it particularly susceptible to overfitting.

The core challenge arises from the algorithm's relentless drive to minimize the loss on the training data. In the initial stages, new trees model the dominant patterns and reduce prediction errors significantly. As the process continues over many iterations, the remaining residuals increasingly represent not just the subtle underlying structure but also the random noise inherent in the training sample. If the base learners are sufficiently complex (e.g., deep decision trees) and the boosting continues unabated, the algorithm begins to fit this noise meticulously. The model essentially starts memorizing the training data, including its idiosyncrasies.

From a bias-variance perspective, gradient boosting aggressively reduces bias by constructing a complex, additive function. Without constraints, this process can lead to extremely high variance. The model becomes exquisitely tuned to the training data but fails to generalize to new, unseen data points because the "patterns" it learned in later stages were merely noise artifacts. This manifests as a characteristic divergence between performance metrics on the training set and a separate validation set. Training error might continue to decrease steadily with more boosting rounds, while validation error reaches a minimum and then starts to increase as the model overfits.

Training error typically continues to decrease with more iterations, while validation error often decreases initially but then starts to rise as the model begins overfitting.

The complexity of the base learners plays a significant role. Decision trees, especially when allowed to grow deep, can create splits that isolate very small numbers of training instances, potentially even single data points. When fitting residuals, such complex trees can easily find splits that perfectly account for the noise associated with these few instances, leading to highly specific rules that do not generalize.

This behavior contrasts with methods like Random Forests (based on bagging), where averaging predictions from multiple independently trained, deep trees helps reduce overall variance. Boosting's sequential nature, where each tree depends on the previous ones, lacks this inherent variance reduction mechanism through simple averaging and instead requires explicit regularization to prevent the variance from escalating.

Understanding these overfitting mechanisms is fundamental. Recognizing that unconstrained boosting will almost inevitably overfit the training data underscores the importance of the regularization techniques discussed throughout the rest of this chapter. These methods provide the necessary controls to harness the power of boosting while ensuring the resulting models generalize well to new challenges.