I have a question about implementing policy gradient methods for problems with continuous action spaces.
Assume that actions are sampled from a diagonal Gaussian distribution with mean vector $\mu$ and standard deviation vector $\sigma$. As far as I understand, we can define a neural network that takes the current state as the input and returns a $\mu$ as its output. According to OpenAI Spinning Up, the standard deviation $\sigma$ can be represented in two different ways:
I don't completely understand the first method. Does it mean that we must set the log standard deviations to fix numbers? Then how do we choose these numbers?