A minimax optimal control approach for robust neural ODEs
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Distributed Implementation of Minimax Adaptive Controller For Finite Set of Linear Systems
This paper deals with a distributed implementation of minimax adaptive control algorithm for networked dynamical systems modeled by a finite set of linear models. To hedge against the uncertainty arising out of finite nu…
When can Regression-Adjusted Control Variate Help? Rare Events, Sobolev Embedding and Minimax Optimality
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of…
When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of…
regressionDistributed Adaptive Control for Uncertain Networks
Control of network systems with uncertain local dynamics has remained an open problem for a long time. In this paper, a distributed minimax adaptive control algorithm is proposed for such networks whose local dynamics ha…
Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes
We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear functi…
reinforcement-learningReinforcement LearningReinforcement Learning (RL)