Hamilton-Jacobi-Bellman Equations for Q-Learning in Continuous Time
Abstract
In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the unique viscosity solution of the HJB equation. A necessary and sufficient condition for optimality is provided using the viscosity solution framework. By using the HJB equation, we develop a Q-learning method for continuous-time dynamical systems. A DQN-like algorithm is also proposed for high-dimensional state and control spaces. The performance of the proposed Q-learning algorithm is demonstrated using 1-, 10- and 20-dimensional dynamical systems.
Cite
@article{arxiv.1912.10697,
title = {Hamilton-Jacobi-Bellman Equations for Q-Learning in Continuous Time},
author = {Jeongho Kim and Insoon Yang},
journal= {arXiv preprint arXiv:1912.10697},
year = {2020}
}
Comments
2nd Annual Conference on Learning for Dynamics and Control (L4DC)