State-value function

upshard

V^{\pi}(s) = \mathbb{E}_{\pi}\!\left[G_t \mid S_t = s\right]

How good a state is: the return you expect from it if you keep following your current policy. It judges the situation, not the choice — which is why it cannot on its own tell you what to do.

Symbols

$V^{\pi}$: The value function under policy pi.
$s$: The state being evaluated.
$\pi$: The policy whose behaviour is being assumed.

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State-value function

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