  In this paper, we propose a deep learning framework for solving
high-dimensional partial integro-differential equations (PIDEs) based on the
temporal difference learning. We introduce a set of Levy processes and
construct a corresponding reinforcement learning model. To simulate the entire
process, we use deep neural networks to represent the solutions and non-local
terms of the equations. Subsequently, we train the networks using the temporal
difference error, termination condition, and properties of the non-local terms
as the loss function. The relative error of the method reaches O(10^{-3}) in
100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump
problems. Additionally, our method demonstrates the advantages of low
computational cost and robustness, making it well-suited for addressing
problems with different forms and intensities of jumps.
