Return (RL)

In a Markov decision process the return $G_t$ at time step $t$ is defined to be the discounted sum of rewards:

$$ > G_t = \sum_{i=1}^{\infty} \gamma^{i-1} R_{t+i} > $$

where $\gamma$ is our discounted factor and the summation goes as high as the length of the run. (Note here $R_{t+i}$ is a random variable as is $G_t$.) Due to the definition of rewards it has a nice recursive property:

$$ > G_t = R_{t+1} + \gamma G_{t+1}. > $$