Q(S_{t}, A_{t}) &\leftarrow Q(S_{t}, A_{t}) + \alpha [R_{t+1} + \gamma E_{\pi}[Q(S_{t+1}, A_{t+1})|S_{t+1}] - Q(S_{t}, A_{t})]\\
&(= Q(S_{t}, A_{t}) + \alpha [R_{t+1} + \gamma \sum\limits_{a \in \mathcal{A}(S_{t+1})} Q(S_{t+1}, a)\pi(a | S_{t+1}) - Q(S_{t}, A_{t}))
\end{aligned}$$
Expected Sarsa uses the expected value over the next state-action pairs, so all actions viable in the state are considered.
Expected Sarsa performs better than [[Sarsa]] in terms of the variance of its [[Return]] but costs more.
