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This paper introduces the Hamilton-Jacobi-Bellman Proximal PolicyOptimization (HJBPPO) algorithm into reinforcement learning. TheHamilton-Jacobi-Bellman (HJB) equation is used in control theory to evaluatethe optimality of the value function. Our work combines the HJB equation withreinforcement learning in continuous state and action spaces to improve thetraining of the value network. We treat the value network as a Physics-InformedNeural Network (PINN) to solve for the HJB equation by computing itsderivatives with respect to its inputs exactly. The Proximal PolicyOptimization (PPO)-Clipped algorithm is improvised with this implementation asit uses a value network to compute the objective function for its policynetwork. The HJBPPO algorithm shows an improved performance compared to PPO onthe MuJoCo environments.

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