论文标题
通过对均值场类型神经网络随机控制的对抗训练的稳定性
Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type
论文作者
论文摘要
在本文中，我们提出了一种通过对抗输入（又称对抗性攻击）的神经网络平均场型控制及其随机稳定性分析的方法。这是一类数据驱动的均值场型控制，其中将变量（例如系统状态和控制输入）的分布纳入了问题。此外，我们提出了一种方法，以通过神经网络验证解决方案近似值的可行性并评估其稳定性。此外，我们通过使用对抗性输入来扩大训练集以获得更强大的神经网络来增强稳定性。最后，提出了一个基于线性二次平均场类型控制问题（LQ-MTC）的练习示例，以说明我们的方法论。
In this paper, we present an approach to neural network mean-field-type control and its stochastic stability analysis by means of adversarial inputs (aka adversarial attacks). This is a class of data-driven mean-field-type control where the distribution of the variables such as the system states and control inputs are incorporated into the problem. Besides, we present a methodology to validate the feasibility of the approximations of the solutions via neural networks and evaluate their stability. Moreover, we enhance the stability by enlarging the training set with adversarial inputs to obtain a more robust neural network. Finally, a worked-out example based on the linear-quadratic mean-field type control problem (LQ-MTC) is presented to illustrate our methodology.
