论文标题
意见动力学随机控制的深图形FBSDE
Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control
论文作者
论文摘要
在本文中，我们提出了一种可扩展的深度学习方法，以解决意见动态随机最佳控制问题，并在动力学和成本函数中使用平均字段期限耦合。我们的方法依赖于汉密尔顿 - 雅各比 - 贝尔曼部分偏微分方程的概率表示。基于Feynman-kac引理的非线性版本，汉密尔顿 - 雅各比 - 贝尔曼局部偏微分方程的解决方案与前向后随机微分方程的解决方案有关。这些方程可以使用新颖的深神经网络进行数值求解，该网络具有针对该问题的架构。根据两极化的共识实验，对所得算法进行了测试。大规模（10K）试验验证了我们算法的可伸缩性和概括性。拟议的框架为未来在极度大规模问题上应用的可能性打开了可能性。
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.
