<p>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&amp;B book page 60:</p>
<blockquote>
<p>The value function <span class="math-container">$v_{\pi}$</span> is the unique solution to its Bellman equation.</p>
</blockquote>
<p><span class="math-container">$v$</span> is the state-value function and <span class="math-container">$\pi$</span> is a given policy as you specified.</p>

CC BY-SA 4.0
2024-03-14T21:51:16.243Z
2024-03-14T21:51:16.243Z
cinch
<p>Is the following statement correct?</p>
<p>&quot;For an MDP and a given policy, the Bellman equation can be used to check the correctness of the state-value function.&quot;</p>

CC BY-SA 4.0
2024-03-14T21:04:38.310Z
What do you mean by ‘correctness’?
David
<reinforcement-learning><markov-decision-process>
MDP and a given policy and the correctness of the state-value function
DSPinfinity
# MDP and a given policy and the correctness of the state-value function

(Asked by: username_0 on 2024-03-14)

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."

**Tags:** reinforcement-learning, markov-decision-process

> **Comments:**
> **username_1**: What do you mean by ‘correctness’?  

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## 1 answers

### Answer by username_2 on 2024-03-14. Score: 0 | Accepted answer

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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