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# Questions tagged [return]

For questions related to the concept of "return" in reinforcement learning.

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### What is the difference between return and expected return?

At a time step $t$, for a state $S_{t}$, the return is defined as the discounted cumulative reward from that time step $t$. If an agent is following a policy (which in itself is a probability ...
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### How can the $\lambda$-return be defined recursively?

The $\lambda$-return is defined as $$G_t^\lambda = (1-\lambda)\sum_{n=1}^\infty \lambda^{n-1}G_{t:t+n}$$ where G_{t:t+n} = R_{t+1}+\gamma R_{t+2}+\dots +\gamma^{n-1}R_{t+n} + \gamma^n\hat{v}(S_{t+n})...
Let's use Excercise 3.8 from Sutton, Barto - Introduction to RL: Suppose $\gamma = 0.5$ and following sequence of rewards is received $R_1=-1$ , $R_2=2$ , $R_3=6$ , $R_4=3$ , $R_5=2$ , with $T=5$ ...
Sutton and Barto 2018 define the discounted return $G_t$ the following way (p 55): Is my interpretation correct? Or should all "1" be in the same column?