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This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by…

Machine Learning · Computer Science 2024-06-04 Kentaro Kanamori , Takuya Takagi , Ken Kobayashi , Yuichi Ike

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to…

Machine Learning · Computer Science 2022-04-25 Aaron Babier , Timothy C. Y. Chan , Adam Diamant , Rafid Mahmood

With the widespread use of machine learning, concerns over its security and reliability have become prevalent. As such, many have developed defenses to harden neural networks against adversarial examples, imperceptibly perturbed inputs that…

Machine Learning · Computer Science 2022-05-09 Pratik Vaishnavi , Kevin Eykholt , Amir Rahmati

In this paper, we address the adversarial training of neural ODEs from a robust control perspective. This is an alternative to the classical training via empirical risk minimization, and it is widely used to enforce reliable outcomes for…

Optimization and Control · Mathematics 2024-04-02 Cristina Cipriani , Alessandro Scagliotti , Tobias Wöhrer

Although the recent progress is substantial, deep learning methods can be vulnerable to the maliciously generated adversarial examples. In this paper, we present a novel training procedure and a thresholding test strategy, towards robust…

Machine Learning · Computer Science 2018-11-08 Tianyu Pang , Chao Du , Yinpeng Dong , Jun Zhu

This paper proposes a classification framework with a rejection option to mitigate the performance deterioration caused by adversarial examples. While recent machine learning algorithms achieve high prediction performance, they are…

Machine Learning · Computer Science 2020-10-27 Masahiro Kato , Zhenghang Cui , Yoshihiro Fukuhara

Adversarial Training (AT) is one of the most effective methods to train robust Deep Neural Networks (DNNs). However, AT creates an inherent trade-off between clean accuracy and adversarial robustness, which is commonly attributed to the…

Computer Vision and Pattern Recognition · Computer Science 2025-08-05 Yanyun Wang , Li Liu

Adversarial training can improve the robustness of neural networks. Previous methods focus on a single adversarial training strategy and do not consider the model property trained by different strategies. By revisiting the previous methods,…

Computer Vision and Pattern Recognition · Computer Science 2023-03-28 Xingbin Liu , Huafeng Kuang , Xianming Lin , Yongjian Wu , Rongrong Ji

The problem of multi-robot target tracking asks for actively planning the joint motion of robots to track targets. In this paper, we focus on such target tracking problems in adversarial environments, where attacks or failures may…

Robotics · Computer Science 2021-09-22 Lifeng Zhou , Vijay Kumar

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…

Machine Learning · Computer Science 2022-11-24 Jimmy Lin , Chudi Zhong , Diane Hu , Cynthia Rudin , Margo Seltzer

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

Machine Learning · Computer Science 2025-11-19 Varun Babbar , Hayden McTavish , Cynthia Rudin , Margo Seltzer

The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…

Optimization and Control · Mathematics 2025-04-28 Dimitris Bertsimas , Berk Öztürk

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

Machine Learning · Computer Science 2026-03-11 Sabino Francesco Roselli , Eibe Frank

Adversarial Training (AT) is one of the most effective methods for developing robust deep neural networks (DNNs). However, AT faces a trade-off problem between clean accuracy and adversarial robustness. In this work, we reveal a surprising…

Computer Vision and Pattern Recognition · Computer Science 2026-04-30 Yanyun Wang , Qingqing Ye , Li Liu , Zi Liang , Haibo Hu

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the…

Machine Learning · Computer Science 2019-12-11 Hongge Chen , Huan Zhang , Si Si , Yang Li , Duane Boning , Cho-Jui Hsieh

In this paper, we propose an optimization-based adversarial attack against Neural Machine Translation (NMT) models. First, we propose an optimization problem to generate adversarial examples that are semantically similar to the original…

Computation and Language · Computer Science 2023-06-16 Sahar Sadrizadeh , Clément Barbier , Ljiljana Dolamic , Pascal Frossard

Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…

Optimization and Control · Mathematics 2020-02-24 Rafael Blanquero , Emilio Carrizosa , Cristina Molero-Río , Dolores Romero Morales

Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…

Machine Learning · Computer Science 2025-10-29 Cristobal Heredia , Pedro Chumpitaz-Flores , Kaixun Hua

Deep neural networks (DNNs) are vulnerable to adversarial examples, in which DNNs are misled to false outputs due to inputs containing imperceptible perturbations. Adversarial training, a reliable and effective method of defense, may…

Computer Vision and Pattern Recognition · Computer Science 2025-11-14 Zongyuan Zhang , Qingwen Bu , Tianyang Duan , Zheng Lin , Yuhao Qing , Zihan Fang , Heming Cui , Dong Huang

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Machine Learning · Computer Science 2024-10-28 Shudian Zhao , Jan Kronqvist