Answers.Body: <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>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-03-14T21:51:16.243Z
Answers.LastActivityDate: 2024-03-14T21:51:16.243Z
Answers.UserDisplayName: cinch
Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-03-14T21:04:38.310Z
Comments.Text: What do you mean by ‘correctness’?
Comments.UserDisplayName: David
Tags: <reinforcement-learning><markov-decision-process>
Title: MDP and a given policy and the correctness of the state-value function
UserDisplayName: DSPinfinity
ThreadText: # 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’?  
  
  ---
  
  ## 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.
  
  
  ---
  
  