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.
Abstract (translated)
这篇文章将哈特利-贾里齐-贝尔曼(HJB)渐进决策优化算法引入到强化学习中。在控制理论中,哈特利-贾里齐-贝尔曼(HJB)方程被用来评估价值函数的最优性。我们的工作将HJB方程与连续状态和行动空间中的强化学习相结合,以提高价值网络的训练质量。我们将价值网络视为一个物理学驱动的神经网络(PINN),通过计算其输入的导数来求解HJB方程。在这个实现中,渐进决策优化(PPO)裁剪算法得到了改进,因为它使用价值网络来计算其策略网络的目标函数。与PPO相比,HJBPPO算法在MuJoCo环境中表现出更好的性能。
URL
https://arxiv.org/abs/2302.00237
