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Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps

Jean-Loup Dupret, Patrick Cheridito · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26718 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Desarrollamos un marco de aprendizaje profundo de Pontryagin para problemas de control estocástico de tiempo continuo de alta dimensión que acomoda naturalmente los saltos-difusiones. A diferencia de la optimización de políticas directas, que diferencia repetidamente el objetivo a través de la dinámica discretizada en todo el tiempo, nuestro método separa el aprendizaje adjunto de la mejora de políticas incorporando explícitamente la información de sensibilidad del estado del principio estocástico de Pontryagin. Para un control fijo de Markov, primero calculamos las etiquetas adjuntas de la ruta mediante la retropropagación de la recompensa a lo largo del tiempo a lo largo de las trayectorias estatales simuladas, y proyectamos estas etiquetas en el estado de Markov a través de un paso de regresión supervisado. El control se actualiza luego

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Pointwise, Mathematics, Optimal control, Pontryagin's minimum principle, Markov chain, Markov process

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