Log-Loss Optimization for Boosting a Nash Equilibrium Decision Tree

Decision trees rank among the most popular classification tools, employed in practical applications due to their known efficiency. A Nash equilibrium-based decision tree splits node data using the Nash equilibrium concept. Boosting is a technique that is used to enhance the performance of a classifier by allowing an in-depth exploration of the data. This paper proposes the use of an AdaBoost model with a log-loss optimization mechanism to improve the performance of an equilibrium-based decision tree. The two-step approach first builds equilibrium decision trees on weighted data; after that, determines the contribution of each classifier by optimizing the overall log-loss function. Numerical experiments illustrate the approach’s performance by comparing results on a set of synthetic and real-world data with state-of-the-art tree-based boosting methods.

决策树是当前最主流的分类工具之一，因其公认的高效性而被广泛应用于各类实际场景中。基于纳什均衡（Nash equilibrium）的决策树则借助纳什均衡概念对节点数据进行划分。提升（Boosting）是一类通过深入挖掘数据特征以提升分类器性能的技术手段。本文提出了一种搭载对数损失（log-loss）优化机制的自适应提升（AdaBoost）模型，用以优化基于纳什均衡的决策树的性能表现。该两步法首先在带权重的数据集上构建纳什均衡决策树，随后通过优化全局对数损失函数，确定各分类器的贡献权重。数值实验通过将本文所提方法在多组合成数据集与真实世界数据集上的实验结果，与当前前沿的基于树结构的提升类算法进行对比，验证了该方法的性能优势。