Temporal Difference Learning for High-Dimensional PIDEs with Jumps
Abstract
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.
Cite
@article{arxiv.2307.02766,
title = {Temporal Difference Learning for High-Dimensional PIDEs with Jumps},
author = {Liwei Lu and Hailong Guo and Xu Yang and Yi Zhu},
journal= {arXiv preprint arXiv:2307.02766},
year = {2024}
}