Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control

04/05/2022
by   Tianrong Chen, et al.
0

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.

READ FULL TEXT
research
06/11/2019

Deep Forward-Backward SDEs for Min-max Control

This paper presents a novel approach to numerically solve stochastic dif...
research
11/30/2019

Applications of the Deep Galerkin Method to Solving Partial Integro-Differential and Hamilton-Jacobi-Bellman Equations

We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spi...
research
06/11/2019

Deep 2FBSDEs for Systems with Control Multiplicative Noise

We present a deep recurrent neural network architecture to solve a class...
research
02/11/2019

Neural Network Architectures for Stochastic Control using the Nonlinear Feynman-Kac Lemma

In this paper we propose a new methodology for decision-making under unc...
research
08/26/2020

Deep Learning for Constrained Utility Maximisation

This paper proposes two algorithms for solving stochastic control proble...
research
11/21/2020

Multi-agent Deep FBSDE Representation For Large Scale Stochastic Differential Games

In this paper, we present a deep learning framework for solving large-sc...
research
07/15/2019

Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

Optimal control problems including partial differential equation (PDE) a...

Please sign up or login with your details

Forgot password? Click here to reset