Q-Learning
Q-Learning
**Q-Learning** is an off-policy temporal difference control algorithm:

$$Q\left(S\_{t}, A\_{t}\right) \leftarrow Q\left(S\_{t}, A\_{t}\right) + \alpha\left[R_{t+1} + \gamma\max\_{a}Q\left(S\_{t+1}, a\right) - Q\left(S\_{t}, A\_{t}\right)\right] $$

The learned action-value function $Q$ directly approximates $q\_{*}$, the optimal action-value function, independent of the policy being followed.

Source: Sutton and Barto, Reinforcement Learning, 2nd Edition