How to obtain the fastest descent trajectory using reinforcement learning methods?

Question

I know the conventional approach is to solve the Euler-Lagrange equations, but I believe the action space in reinforcement learning can be treated as a function space, and then set up a reward function. Therefore, I think it should be possible to use reinforcement learning methods to obtain the fastest descent trajectory. However, I'm unsure about the specific details of how to handle it. On the other hand, perhaps this can be viewed as an unconstrained optimization problem. I will be very grateful for everyone's help.