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 input perturbations. Neural ODEs allow the interpretation of deep neural networks as discretizations of control systems, unlocking powerful tools from control theory for the development and the understanding of machine learning. In this specific case, we formulate the adversarial training with perturbed data as a minimax optimal control problem, for which we derive first order optimality conditions in the form of Pontryagin's Maximum Principle. We provide a novel interpretation of robust training leading to an alternative weighted technique, which we test on a low-dimensional classification task.

本文基于鲁棒控制的视角讨论神经ODE的对抗训练，引入了一种替代经验风险最小化的方法，通过可靠处理输入扰动来实现可靠结果。将深度神经网络解释为控制系统离散化，利用控制理论的强大工具来开发和理解机器学习。我们将带有扰动数据的对抗性训练描述为极小极大最优控制问题，并推导出Pontryagin's Maximum Principle形式的一阶最优性条件。我们提供了鲁棒训练的新解释，提出了一种替代加权技术，并在低维分类任务上进行了测试。

一个极小极大优化控制方法用于稳健神经ODE