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DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems

arXiv 2511.04309 ↗First posted 6 Nov 2025math.NA cs.LG cs.NAcited by 0

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Abstract (arXiv)

We consider numerical resolution of principal-agent (PA) problems in continuous time. We formulate a generic PA model with continuous and lump payments and a multi-dimensional strategy of the agent. To tackle the resulting Hamilton-Jacobi-Bellman equation with an implicit Hamiltonian we develop a novel deep learning method: the Deep Principal-Agent Actor Critic (DeepPAAC) Actor-Critic algorithm. DeepPAAC is able to handle multi-dimensional states and controls, as well as constraints. We investigate the role of the neural network architecture, training designs, loss functions, etc. on the convergence of the solver, presenting five different case studies.

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References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
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  3. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  4. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 135
  5. 2021Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networkscited by 27
  6. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 19
  7. 2019Extensions of the Deep Galerkin Methodcited by 10
  8. 2024Policy Iteration for Exploratory Hamilton--Jacobi--Bellman Equationscited by 9
  9. 2020A modified MSA for stochastic control problemscited by 8
  10. 2022Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problemscited by 6
  11. 2025Deep Learning for Continuous-Time Stochastic Control with Jumpscited by 6
  12. 2015Dynamic programming approach to principal-agent problemscited by 5
5 more
  1. 2021Deep Learning for Principal-Agent Mean Field Gamescited by 5
  2. 2019Relaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systemscited by 4
  3. 2023A Machine Learning Method for Stackelberg Mean Field Gamescited by 4
  4. 2024Convergence Analysis for Entropy-Regularized Control Problems: A Probabilistic Approachcited by 4
  5. 2025Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studiescited by 3

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