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

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

“…Moreover, the recent progress on machine learning technologies made it easier to test and provide more efficient approximations of the solutions to complex mean-field type control problems. The link between deep learning and control/games problems was recently studied by a number of others in series of papers (see, e.g., [16][17][18][19][20][21][22][23]), where the authors (jointly and/or independently) proposed algorithms for the solution of mean-field optimal control problems based on approximations of the theoretical solutions by neural networks, using the software package TensorFlow with its "Stochastic Gradient Descent" optimizer designed for machine learning. However, to the best of our knowledge, the mean-field type game case and the related stability of the associated neural networks were not considered in the literature so far.…”

“…In deep learning, there is an increasing interest in studying and improving the robustness and stability of the trained neural networks; see, for example, [18,24,25], where it has been reported that a simple modification in the input data might fool a well-trained neural network, returning a wrong output. For instance, a picture that is previously well classified by a trained neural network could be incorrectly classified once we perturb one or more pixels in it.…”