Boosting learning rate and tree count

Why should learning rate and number of boosting rounds be tuned together?

Each boosting update is multiplied by the learning rate, so smaller steps usually need more rounds to reach comparable fit. Their interaction affects both optimisation and regularisation. Tree depth and leaf constraints also change each update's capacity. Choose combinations or use early stopping inside development folds, then assess on outer periods. A smaller learning rate with enough rounds can still overfit.