A minimax optimal control approach for robust neural ODEs
This provides a control-theoretic approach to robust neural ODE training, though it appears incremental with limited testing.
The authors tackled adversarial training of neural ODEs by formulating it as a minimax optimal control problem, deriving Pontryagin's Maximum Principle optimality conditions and testing an alternative weighted technique on a low-dimensional classification task.
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.