Machine learning for partial differential equations (PDEs) is a hot topic. In this paper we introduce and analyse a Deep BSDE scheme for nonlinear integro-PDEs with unbounded nonlocal operators -problems arising in e.g. stochastic control and games involving infinite activity jump-processes. The scheme is based on a stochastic forward-backward SDE representation of the solution of the PDE and (i) approximation of small jumps by a Gaussian process, (ii) simulation of the forward part, and (iii) a neural net regression for the backward part. Unlike grid-based schemes, it does not suffer from the curse of dimensionality and is therefore suitable for high dimensional problems. The scheme is designed to be convergent even in the infinite activity/unbounded nonlocal operator case. A full convergence analysis is given and constitutes the main part of the paper.

翻译：偏微分方程（PDE）的机器学习是一个热门课题。本文针对具有无界非局部算子的非线性积分-偏微分方程——这类问题出现在例如涉及无限活动性跳跃过程的随机控制和博弈中——提出并分析了一种深度BSDE方案。该方案基于PDE解的随机正向-反向SDE表示，并包含：（i）用高斯过程近似小跳跃；（ii）正向部分的模拟；以及（iii）反向部分的神经网络回归。与基于网格的方案不同，它不受维度灾难的影响，因此适用于高维问题。该方案被设计为即使在无限活动性/无界非局部算子情况下也能收敛。本文给出了完整的收敛性分析，这构成了论文的主要部分。