In the answer I'll be using notation similar to the one from the SAC paper. If we look at the standard objective function for policy gradient methods we have \begin{align} J_\pi &= V_\pi(s_t)\\ &= \mathbb E_{a_t \sim \pi(a|s_t)}[Q(s_t, a_t)]\\ &= \mathbb E_{a_t \sim \pi(a|s_t)}[ \mathbb E_{s_{t+1} \sim p(s|s_t, a_t)} [r(s_t, a_t) + V(s_{t+1})]]\\ ...


I'll give it a go here and try to answer your question, I'm not sure if this is entirely correct, so if someone thinks that it isn't please correct me. I'll disregard expectation here to make things simpler. First, note that policy $\pi$ depends on parameter vector $\phi$ and function $f_\phi(\epsilon_t;s_t)$, and value function $Q$ depends on parameter ...


Yes you can map the output onto [0,1] as you indicate. You should treat this as a modification to the environment. I.e. imagine that the environment takes actions in [-1, 1] instead of [0,1]. No you don't need to change any equations.

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