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Is the following statement correct?

"For an MDP and a given policy, the Bellman equation can be used to check the correctness of the state-value function."

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    $\begingroup$ What do you mean by ‘correctness’? $\endgroup$
    – David
    Commented Mar 14 at 21:04

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Generally speaking it's correct. Bellman equation is a set of linear equations rather than a single equation for the usual tabular cases. If we put these equations together, it would be clear how to calculate all the state values. See S&B book page 60:

The value function $v_{\pi}$ is the unique solution to its Bellman equation.

$v$ is the state-value function and $\pi$ is a given policy as you specified.

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