Efficient non-greedy optimization of decision trees

TL;DR

This paper introduces a global optimization algorithm for decision trees that jointly optimizes all split functions and leaf parameters, leading to better performance than traditional greedy methods.

Contribution

It presents a novel non-greedy training algorithm for decision trees based on a convex upper bound and stochastic gradient descent, enabling deep tree training.

Findings

Outperforms greedy decision trees on multiple benchmarks

Enables training of deeper trees efficiently

Uses a convex surrogate for global optimization

Abstract

Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. The run-time of computing the gradient of the proposed surrogate objective with respect to each training exemplar is quadratic in the the tree depth, and thus training deep trees is feasible. The use of stochastic gradient descent for optimization enables effective training with large datasets. Experiments on several classification benchmarks demonstrate that the resulting non-greedy decision trees outperform greedy decision tree baselines.