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

TL;DR

DeepPAAC introduces a novel deep learning algorithm to numerically solve complex principal-agent problems modeled by Hamilton-Jacobi-Bellman equations, accommodating multi-dimensional strategies and constraints.

Contribution

The paper develops DeepPAAC, a new deep learning-based Actor-Critic method specifically designed for solving high-dimensional principal-agent problems in continuous time.

Findings

DeepPAAC effectively handles multi-dimensional states and controls.

The method demonstrates convergence across five case studies.

Neural network architecture impacts solver performance.

Abstract

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.