Online Learning/Continual Learning for tree-based Algorithms

Every example I come across any kind of iterative learning on Random Forest/XGBoost/LightGBM, it just continuously grows the number of estimators for new batches of data by n_tree/n_estimators/num_boost_rounds every time .fit() gets applied [...]. Most of them seem to rely on iterative learning for training on very large datasets that can't be loaded into memory at once.

However, I want to implement a continuous learning pipeline (with LightGBM; Python) that takes newly available data on a daily basis in order to update an existing model (without the need to retrain on the whole [growing] dataset; stateful). The initially mentioned approach would imply that my model will ever increase its tree count.

Is it possible to train tree-based algorithms so that the estimators (split thresholds) themselves get updated/adjusted in contrast to only adding estimators?

This is a really good question for which I will give you a theoretical result; in particular, I am not aware of any specific implementation in any programming language.

The concept of incremental learning with decision trees started in 1986 to enhance the ID3 learning algorithm to learn continually/incrementally (recall that ID3 deals only with categorical input features/variables); the resulting procedure is called ID4.

Some years later, Utgoff et al. proposed other two approaches (ID5 and ITI) to overcome some of the shortcomings of the ID4 approach.