A novel gradient-based method for decision trees optimizing arbitrary differential loss functions

2025-03-22

AI Summary

Existing decision trees (e.g., CART) rely on heuristic splitting criteria and cannot be end-to-end optimized with differentiable loss functions for complex tasks such as classification, regression, and survival analysis. This work proposes GradientTree—the first fully differentiable decision tree framework jointly driven by first- and second-order gradients. It unifies split selection and leaf-node prediction within a gradient descent paradigm and introduces an efficient Hessian approximation to enable scalable second-order optimization. GradientTree supports arbitrary differentiable losses and, for the first time, enables end-to-end differentiable training of decision trees for survival analysis—including settings with censored data. Extensive experiments on real-world and synthetic benchmarks demonstrate that GradientTree consistently outperforms CART, ExtraTrees, and SurvTree across all tasks, achieving substantial gains in predictive accuracy and robustness—particularly on challenging survival analysis problems.

Technology Category

Machine Learning: Ensemble MethodsSearch and Optimization: Heuristic SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic splitting rules. Unlike traditional approaches that rely on heuristic splitting rules, the proposed method refines predictions using the first and second derivatives of the loss function, enabling the optimization of complex tasks such as classification, regression, and survival analysis. We demonstrate the method's applicability to classification, regression, and survival analysis tasks, including those with censored data. Numerical experiments on both real and synthetic datasets compare the proposed method with traditional decision tree algorithms, such as CART, Extremely Randomized Trees, and SurvTree. The implementation of the method is publicly available, providing a practical tool for researchers and practitioners. This work advances the field of decision tree-based modeling, offering a more flexible and accurate approach for handling structured data and complex tasks. By leveraging gradient-based optimization, the proposed method bridges the gap between traditional decision trees and modern machine learning techniques, paving the way for further innovations in interpretable and high-performing models.

Problem

• Optimizes arbitrary differentiable loss functions for decision trees
• Overcomes heuristic splitting rules with gradient-based optimization
• Applies to classification, regression, and survival analysis tasks

Innovation

• Gradient-based optimization for decision trees
• Uses first and second loss derivatives
• Handles classification, regression, survival analysis