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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

Japanese

我々は、高次元の継続的時間ストーカスコントロールの問題のための深いPontryagin学習枠組みを開発し、自然にジャンプ拡散を可能にする。直接的なポリシー最適化とは異なり、全時間の差別化ダイナミクスを通じて目標を繰り返し区別するため、我々の方法は、Pontryaginのストーカスティック最大原則からの状態敏感性情報を明示的に組み込むことによって、政策改善から補助学習を分離します。固定マルコフ制御のために、我々は最初に、シミュレーションされたステータス軌道に沿って時間を通して報酬をバックプロパガンダントし、これらのラベルをマルコフ状態にプロジェクトし、監督された回帰段

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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