N-step Returns
N-step Returns
**$n$-step Returns** are used for value function estimation in reinforcement learning. Specifically, for $n$ steps we can write the complete return as:

$$ R\_{t}^{(n)} = r\_{t+1} + \gamma{r}\_{t+2} + \cdots + \gamma^{n-1}\_{t+n} + \gamma^{n}V\_{t}\left(s\_{t+n}\right) $$

We can then write an $n$-step backup, in the style of TD learning, as:

$$ \Delta{V}\_{r}\left(s\_{t}\right) = \alpha\left[R\_{t}^{(n)} - V\_{t}\left(s\_{t}\right)\right] $$

Multi-step returns often lead to faster learning with suitably tuned $n$.

Image Credit: Sutton and Barto, Reinforcement Learning