Stackelberg Mean-Field-Type Games with Polynomial Cost

Frihi, Zahrate El Oula; Barreiro-Gómez, Julian; Choutri, Salah Eddine; Djehiche, Boualem; Tembiné, Hamidou

doi:10.1016/j.ifacol.2020.12.1234

Cited by 2 publications

(5 citation statements)

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“…The solution to Problem ( 12) is to find an initial condition for the system state, x(t 0 ) ∶= x(t 0 ) ∈  𝛼 , such that the set of trained neural networks for the decision-makers g θ  is unable to stabilize the system in (11). Problem ( 12) can be solved by using, for example, the projected gradient descent (PGD) algorithm as follows:…”

Section: Finding Adversarial Initial Statesmentioning

confidence: 99%

“…where Proj  𝛼 (•) denotes the projection onto the set  𝛼 and 𝛽 denotes the step size for the gradient algorithm. The stopping condition is when the system state, following (11) with initial condition x(t 0 ) = 𝑦 m , diverges, that given that the dynamics in (11) diverges with initial condition x(t 0 ) = 𝑦 3 . Therefore, this is an adversarial x(t 0 ) = 𝑦 3 .…”

Section: Finding Adversarial Initial Statesmentioning

confidence: 99%

“…Further details about mean-field type control problems can be found in [9]. For applications related to mean-field type control and games problems, we cite, among many others, [10,Chapter 16], [11][12][13], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, this is an adversarial x(t 0 ) = 𝑦 3 . In the contrary, the dynamics in(11) are almost surely stochastically stable for initial conditions x(t 0 ) ∈ {𝑦 , 𝑦 , 𝑦 0 1 2 }.…”

mentioning

confidence: 99%

“…FIGURE 3Evolution example of the PGD, which stops at m = 3 given that the dynamics in(11) diverges with initial condition x(t 0 ) = 𝑦 3 . Therefore, this is an adversarial x(t 0 ) = 𝑦 3 .…”

mentioning

confidence: 99%

See 4 more Smart Citations

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

Barreiro-Gómez

Choutri

2023

Asian Journal of Control

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We 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.

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Section: Finding Adversarial Initial Statesmentioning

confidence: 99%

Section: Finding Adversarial Initial Statesmentioning

confidence: 99%