Gradient Boosting with Piece-Wise Linear Regression Trees

Gradient Boosted Decision Trees (GBDT) is a very successful ensemble learning algorithm widely used across a variety of applications. Recently, several variants of GBDT training algorithms and implementations have been designed and heavily optimized in some very popular open sourced toolkits including XGBoost, LightGBM and CatBoost. In this paper, we show that both the accuracy and efficiency of GBDT can be further enhanced by using more complex base learners. Specifically, we extend gradient boosting to use piecewise linear regression trees (PL Trees), instead of piecewise constant regression trees, as base learners. We show that PL Trees can accelerate convergence of GBDT and improve the accuracy. We also propose some optimization tricks to substantially reduce the training time of PL Trees, with little sacrifice of accuracy. Moreover, we propose several implementation techniques to speedup our algorithm on modern computer architectures with powerful Single Instruction Multiple Data (SIMD) parallelism. The experimental results show that GBDT with PL Trees can provide very competitive testing accuracy with comparable or less training time.