Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps
Abstract
We develop a deep Pontryagin learning framework for high-dimensional continuous-time stochastic control problems that naturally accommodates jump-diffusions. In contrast to direct policy optimization, which repeatedly differentiates the objective through the entire time-discretized dynamics, our method separates adjoint learning from policy improvement by explicitly incorporating state-sensitivity information from the Pontryagin stochastic maximum principle. For a fixed Markov control, we first compute pathwise adjoint labels by backpropagating the reward through time along simulated state trajectories, and project these labels onto the Markov state through a supervised regression step. The control is then updated by enforcing the pointwise Hamiltonian stationarity condition. We prove that the resulting projected adjoint process satisfies a discrete-time Pontryagin principle and converges, as the time step tends to zero, to the solution of the corresponding continuous-time adjoint backward stochastic differential equation. Numerical experiments illustrate the accuracy, stability, and scalability of the approach.
Related
- Reinforcement learning for constrained stochastic linear--quadratic control in continuous time
- Stochastic Riccati equations with jumps for indefinite linear-quadratic control: A stochastic value-flow approach
- On the Pontryagin Maximum Principle for Rough Stochastic Differential Equations
- Continuous Policy and Value Iteration for Stochastic Control Problems with Inhomogeneous Synchronous Coupling
- Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies
BibTeX
@misc{dupret2026deep,
title = {{Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps}},
author = {Jean-Loup Dupret and Patrick Cheridito},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26718},
eprint = {2610.26718},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26718},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps
AU - Jean-Loup Dupret
AU - Patrick Cheridito
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26718
UR - https://arxiv.org/abs/2610.26718
AB - We develop a deep Pontryagin learning framework for high-dimensional continuous-time stochastic control problems that naturally accommodates jump-diffusions. In contrast to direct policy optimization, which repeatedly differentiates the objective through the entire time-discretized dynamics, our method separates adjoint learning from policy improvement by explicitly incorporating state-sensitivity information from the Pontryagin stochastic maximum principle. For a fixed Markov control, we first compute pathwise adjoint labels by backpropagating the reward through time along simulated state trajectories, and project these labels onto the Markov state through a supervised regression step. The control is then updated by enforcing the pointwise Hamiltonian stationarity condition. We prove that the resulting projected adjoint process satisfies a discrete-time Pontryagin principle and converges, as the time step tends to zero, to the solution of the corresponding continuous-time adjoint backward stochastic differential equation. Numerical experiments illustrate the accuracy, stability, and scalability of the approach.
ER -