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Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps

Jean-Loup Dupret, Patrick Cheridito · 2026 · arXiv

DOI: 10.48550/arXiv.2610.26718 · open-access PDF

Indonesian

Kami mengembangkan kerangka kerja pembelajaran Pontryagin yang mendalam untuk masalah kontrol stochastic waktu berkelanjutan yang berdimensi tinggi yang secara alami mengakomodasi lompatan-difusi. Tidak seperti optimasi kebijakan langsung, yang berulang kali membedakan tujuan melalui seluruh dinamika waktu-discretized, metode kami memisahkan pembelajaran tambahan dari peningkatan kebijakan dengan secara eksplisit menggabungkan informasi sensitivitas negara dari prinsip stochastic maksimum Pontryagin.

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 tra

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