In recent years, there has been growing interest in developing robust machine learning (ML) models that can withstand adversarial attacks, including one of the most widely adopted, efficient, and interpretable ML algorithms-decision trees (DTs). This paper proposes a novel coevolutionary algorithm (CoEvoRDT) designed to create robust DTs capable of handling noisy high-dimensional data in adversarial contexts. Motivated by the limitations of traditional DT algorithms, we leverage adaptive coevolution to allow DTs to evolve and learn from interactions with perturbed input data. CoEvoRDT alternately evolves competing populations of DTs and perturbed features, enabling construction of DTs with desired properties. CoEvoRDT is easily adaptable to various target metrics, allowing the use of tailored robustness criteria such as minimax regret. Furthermore, CoEvoRDT has potential to improve the results of other state-of-the-art methods by incorporating their outcomes (DTs they produce) into the initial population and optimize them in the process of coevolution. Inspired by the game theory, CoEvoRDT utilizes mixed Nash equilibrium to enhance convergence. The method is tested on 20 popular datasets and shows superior performance compared to 4 state-of-the-art algorithms. It outperformed all competing methods on 13 datasets with adversarial accuracy metrics, and on all 20 considered datasets with minimax regret. Strong experimental results and flexibility in choosing the error measure make CoEvoRDT a promising approach for constructing robust DTs in real-world applications.

翻译：近年来，开发能够抵御对抗攻击的鲁棒机器学习（ML）模型日益受到关注，其中决策树（DT）作为应用最广泛、高效且可解释性强的算法之一备受关注。本文提出一种新型协同进化算法（CoEvoRDT），旨在构建能够处理对抗场景中含噪声高维数据的鲁棒决策树。受传统决策树算法局限性的启发，我们利用自适应协同进化使决策树能够通过与扰动输入数据的交互实现演化与学习。CoEvoRDT交替进化决策树种群与扰动特征种群，从而构建具有理想特性的决策树。该算法易于适配不同目标指标，支持采用如最小化最大遗憾等定制化鲁棒性准则。此外，通过将其他前沿方法生成的决策树纳入初始种群并在协同进化过程中进行优化，CoEvoRDT有望提升这些方法的最终效果。受博弈论启发，CoEvoRDT利用混合纳什均衡增强收敛性。该方法在20个常用数据集上完成测试，与4种前沿算法相比展现出优越性能：在13个数据集的对抗精度指标上优于所有对比方法，在全部20个数据集的最小化最大遗憾指标上均表现最佳。优异的实验结果与误差度量选择的灵活性，使CoEvoRDT成为构建面向真实场景鲁棒决策树的可行方案。