Quality function (RL)

Similar to the value function a quality function accounts for both state and action. So functionally $q: S \times A \rightarrow \mathbb{R}$ this is the quality of taking action $a \in A$ when you are in state $s \in S$.

Given a policy $\pi$ we can calculate the ideal quality function to be

$$ > q^{\pi}(s,a) = \mathbb{E}_{\pi}[G_t \vert S_t = s, A_t = a]. > $$