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

arXiv: https://arxiv.org/abs/2210.00874 · HTML: https://mlsanity.com/paper/2210.00874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case](https://mlsanity.com/paper/1908.01613/) (2019)
- [Deep Learning Methods for Mean Field Control Problems with Delay](https://mlsanity.com/paper/1905.00358/) (2019)
- [Numerical Methods for Mean Field Games and Mean Field Type Control](https://mlsanity.com/paper/2106.06231/) (2021)
- [Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method](https://mlsanity.com/paper/1611.02023/) (2016)
- [Numerical Methods for Mean-Field-Type Optimal Control Problems](https://mlsanity.com/paper/1703.10001/) (2017)

## Abstract (arXiv)

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.