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

arXiv: https://arxiv.org/abs/2511.04309 · HTML: https://mlsanity.com/paper/2511.04309/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks](https://mlsanity.com/paper/2102.11379/) (2021)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Policy Iteration for Exploratory Hamilton--Jacobi--Bellman Equations](https://mlsanity.com/paper/2406.00612/) (2024)
- [Extensions of the Deep Galerkin Method](https://mlsanity.com/paper/1912.01455/) (2019)
- [A modified MSA for stochastic control problems](https://mlsanity.com/paper/2007.05209/) (2020)
- [Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problems](https://mlsanity.com/paper/2209.07059/) (2022)
- [Convergence Analysis for Entropy-Regularized Control Problems: A Probabilistic Approach](https://mlsanity.com/paper/2406.10959/) (2024)
- [Deep Learning for Continuous-Time Stochastic Control with Jumps](https://mlsanity.com/paper/2505.15602/) (2025)
- [Dynamic programming approach to principal-agent problems](https://mlsanity.com/paper/1510.07111/) (2015)
- [Deep Learning for Principal-Agent Mean Field Games](https://mlsanity.com/paper/2110.01127/) (2021)
- [Relaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems](https://mlsanity.com/paper/1909.05402/) (2019)
- [A Machine Learning Method for Stackelberg Mean Field Games](https://mlsanity.com/paper/2302.10440/) (2023)
- [Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies](https://mlsanity.com/paper/2507.06428/) (2025)

## 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.