Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control
This provides a scalable solution for controlling large-scale opinion dynamics systems, though it appears incremental as an application of existing FBSDE methods to a specific domain.
The paper tackles opinion dynamics stochastic optimal control problems with mean field coupling by developing a scalable deep learning approach based on Forward-Backward Stochastic Differential Equations, achieving validation on a polarized opinion consensus experiment with 10K agents.
In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic representation of the solution of the Hamilton-Jacobi-Bellman partial differential equation. Grounded on the nonlinear version of the Feynman-Kac lemma, the solutions of the Hamilton-Jacobi-Bellman partial differential equation are linked to the solution of Forward-Backward Stochastic Differential Equations. These equations can be solved numerically using a novel deep neural network with architecture tailored to the problem in consideration. The resulting algorithm is tested on a polarized opinion consensus experiment. The large-scale (10K) agents experiment validates the scalability and generalizability of our algorithm. The proposed framework opens up the possibility for future applications on extremely large-scale problems.