# Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control

arXiv: https://arxiv.org/abs/2204.02506 · HTML: https://mlsanity.com/paper/2204.02506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games](https://mlsanity.com/paper/1912.01809/) (2019)
- [Polarization in Geometric Opinion Dynamics](https://mlsanity.com/paper/2106.12459/) (2021)
- [Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs](https://mlsanity.com/paper/1902.03986/) (2019)
- [Learning Optimal Control via Forward and Backward Stochastic Differential Equations](https://mlsanity.com/paper/1509.02195/) (2015)
- [Convergence of Deep Fictitious Play for Stochastic Differential Games](https://mlsanity.com/paper/2008.05519/) (2020)
- [Steering Social Activity: A Stochastic Optimal Control Point Of View](https://mlsanity.com/paper/1802.07244/) (2018)
- [Deep Forward-Backward SDEs for Min-max Control](https://mlsanity.com/paper/1906.04771/) (2019)
- [Large-Scale Multi-Agent Deep FBSDEs](https://mlsanity.com/paper/2011.10890/) (2020)
- [Constrained Sampling-based Trajectory Optimization using Stochastic Approximation](https://mlsanity.com/paper/1911.04621/) (2019)
- [Robust Mean Field Social Control Problems with Applications in Analysis of Opinion Dynamics](https://mlsanity.com/paper/2002.12040/) (2020)
- [On the optimal control of opinion dynamics on evolving networks](https://mlsanity.com/paper/1511.00145/) (2015)
- [Linear-Quadratic Mean Field Social Optimization with a Major Player](https://mlsanity.com/paper/1904.03346/) (2019)
- [The Paradox of Information Access: On Modeling Social-Media-Induced Polarization](https://mlsanity.com/paper/2004.01106/) (2020)

## Built on by (most cited first, 1 of 1)

- [Deep Momentum Multi-Marginal Schr"odinger Bridge](https://mlsanity.com/paper/2303.01751/) (2023)

## Abstract (arXiv)

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.