Data‐driven stability of stochastic mean‐field type games via noncooperative neural network adversarial training

Abstract

AbstractWe propose an approach to neural network stochastic differential games of mean‐field type and its corresponding stochastic stability analysis by means of adversarial training (aka adversarial attacks). This is a class of data‐driven differential games where the distribution of the variables such as the system states and the decision‐makers' strategies (control inputs) is incorporated into the problem. This work casts the cooperative/noncooperative game terminology into the deep learning framework where we talk about cooperative and noncooperative neural network computations that involve learning capabilities and neural network architectures. We suggest a method to computationally validate the feasibility of the approximated solutions via neural networks and evaluate the stochastic stability of the associated closed‐loop system (state feedback Nash). Moreover, we enhance the stochastic stability by enlarging the training set with adversarial initial states to obtain a more robust neural network for a particular decision‐maker. Finally, a worked‐out example based on the linear‐quadratic mean‐field type game (LQ‐MTG) that illustrates our methodology is presented.