policy-indexed action-value function

$$q_{\pi }(s,a)={\mathbb{E}}_{\pi }[G_t|S_t=s,A_t=a]$$

The policy-indexed action-value function $q_{\pi }(s,a)$ is the expected total future reward $G_t$ an agent should receive on if it takes action $a$ at state $s$ and then follows the policy function $\pi$ til the end (excludes $R_t$) in an MDP. This reflects whether an action has long-term benefits in a given state.