Learning Rate vs Tree Count Trade-off

Two engineers are configuring a LightGBM model for a fraud detection task:

• Engineer A: learning_rate=0.3, n_estimators=100
• Engineer B: learning_rate=0.01, n_estimators=3000

Both models train to similar training loss. Engineer B's model has noticeably better validation AUC.

1. Explain mechanistically why Engineer B's configuration generalizes better.
2. What is the mathematical relationship between learning rate and the number of trees needed?
3. Is there a scenario where Engineer A's configuration is preferable?