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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

Korean

우리는 고차원적인 연속 시간 스토카스틱 제어 문제를 위한 깊은 Pontryagin 학습 프레임 워크를 개발합니다. 직접 정책 최적화와는 달리, 전체 시간 분리된 역학을 통해 목표를 반복적으로 차별화하는, 우리의 방법은 Pontryagin 스토카스틱 최대 원칙의 상태 민감성 정보를 명시적으로 통합함으로써 정책 개선에서 보조 학습을 분리합니다. 고정 Markov 제어를 위해, 우리는 먼저 시뮬레이션 상태 경로를 따라 시뮬레이션된 시간을 통해 보상을 반영함으로써 경로를 계산하여 보조 라벨을 계산하고, 감독된 회귀 단계를 통해 Markov 상태로 이러한 라벨을 프로젝션합니다. 컨트롤은 Hamiltonian 포인트 스토카스틱 최대 조건을 강요함

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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