Discounted return

upshard

G_t = \sum_{k=0}^{\infty} \gamma^{k} r_{t+k+1}

The total future reward from a point onwards, with later rewards worth less. The discount both encodes impatience and keeps the sum finite on tasks that never end.

Symbols

$G_t$: The return from time t onwards.
$\gamma$: The discount factor, between zero and one.
$r$: The reward collected at a single step.

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Discounted return

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