Bridging Physics-Informed Neural Networks with Reinforcement Learning: Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO)

Amartya Mukherjee, Jun Liu

Keywords: Continuous-Time Reinforcement Learning, Physics-Informed Neural Networks, Proximal Policy Optimization, Hamilton-Jacobi-Bellman Equation

TL;DR: We introduce the HJBPPO reinforcement learning algorithm that treats the value function as a physics-informed neural network (PINN) to solve the Hamilton-Jacobi-Bellman (HJB) equation for optimal control.

Abstract: This paper introduces the Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO) algorithm into reinforcement learning. The Hamilton-Jacobi-Bellman (HJB) equation is used in control theory to evaluate the optimality of the value function. Our work combines the HJB equation with reinforcement learning in continuous state and action spaces to improve the training of the value network. We treat the value network as a Physics-Informed Neural Network (PINN) to solve for the HJB equation by computing its derivatives with respect to its inputs exactly. The Proximal Policy Optimization (PPO)-Clipped algorithm is improvised with this implementation as it uses a value network to compute the objective function for its policy network. The HJBPPO algorithm shows an improved performance compared to PPO on the MuJoCo environments.

Submission Number: 7