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We know that sklearn's implemenation of AdaBoost algorithm uses DecisionTreeClassifier as the base learner.

Conceptually, AdaBoost assigns equal weights to all examples initially, where the weight is equal to 1/n. n- the number of examples.

But then the AdaBoost documentantion includes a hyperparameter learning_rate defined as:

learning_rate float, default=1.

Weight applied to each classifier at each boosting iteration. A higher learning rate increases the contribution of each classifier. There is a trade-off between the learning_rate and n_estimators parameters.

But then Decision Trees do not use learning_rate parameter since it not a gradient-based model learning approach. Besides, AdaBoost already assigns 1/n to each sample. How then the definition of learning_rate defined in the documentation fits here?

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The learning rate is just applied to each of the tree's predictions and has nothing to do with the tree model itself but the boosting 'meta' algorithm.

Since boosting is iteratively learning from the past model it can overfit so the learning rate is a simple way to control for that. So after each fit that round's predictions is equal to the previous round plus the learning rate multiplied by this iteration's fit. That is the point of the last sentence in the documentation:

There is a trade-off between the learning_rate and n_estimators parameters.

If you have a lower learning rate such as .1 you could have more estimators since each individual estimator is contributing less.

As a side note I have seen it heavily used much more aggressively in gradient boosting.

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