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Solving a class of stochastic optimal control problems by physics-informed neural networks

arXiv 2402.15592 ↗First posted 23 Feb 2024math.OC cs.LGcited by 1

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Abstract (arXiv)

The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the feedback control and the value function using a decoupled neural network with multiple outputs. We train this network by using a loss function with penalty terms that enforce the HJB equation along the sampled trajectories generated by the controlled system. More significantly, numerical results on various applications are carried out to demonstrate that the proposed approach is efficient and applicable.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 23 references that are in the map. First posted on arXiv 23 Feb 2024.

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9 of 23 references.

References · 9

  1. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 82
  2. 2016Deep Learning Approximation for Stochastic Control Problemscited by 55
  3. 2019Deep Learning Methods for Mean Field Control Problems with Delaycited by 25
  4. 2018Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysiscited by 24
  5. 2022A Neural Network Approach for Stochastic Optimal Controlcited by 13
  6. 2015Learning Optimal Control via Forward and Backward Stochastic Differential Equationscited by 11
  7. 2020Solving stochastic optimal control problem via stochastic maximum principle with deep learning methodcited by 6
  8. 2020Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solvercited by 4
  9. 2019Deep 2FBSDEs For Systems With Control Multiplicative Noisecited by 1

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