Stability Via Adversarial Training of Neural Network Stochastic Control of Mean-Field Type

TL;DR

This paper introduces a neural network approach for mean-field-type control systems, analyzing their stochastic stability through adversarial training to improve robustness and validate solution feasibility.

Contribution

It presents a novel methodology combining adversarial training with neural network-based mean-field control and stability validation.

Findings

Enhanced stability with adversarial training

Feasibility of neural network approximations validated

Application to linear-quadratic mean-field control

Abstract

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.