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Evaluating value functions in RL


What is the Q function and what is the V function in reinforcement learning?Reward dependent on (state, action) versus (state, action, successor state)Cannot see what the “notation abuse” is, mentioned by author of bookHow is that possible that a reward function depends both on the next state and an action from current state?state-action-reward-new state: confusion of termsRegarding the Value function in Proximal Policy OptimizationNeed help in deriving Policy Evaluation (Prediction)What is the optimal value of a Markov Decision process with Single actions at each state?How is Importance-Sampling Used in Off-Policy Monte Carlo Prediction?RL Advantage function why A = Q-V instead of A=V-Q?













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I'm working my way through the book Reinforcement Learning by Richar S. Sutton and Andrew G. Barto and I am stuck on the following question.



The value of a state depends on the the values of the actions possible in that state and on how likely each action is to be taken under the current policy.
We can think of this in terms of a small backup diagram rooted at the state and considering each possible action:



enter image description here



Give the equation corresponding to this intuition and diagram for the value at the root node
formula2, in terms of the value at the expected leaf node,
formula, given
formula3. This expectation depends on the policy,
formula4. Then give a second equation in which the expected value is written out explicitly in terms of
formula5such that no expected value notation appears in the equation.



I should mention that...



formula7
...



Where...



formula6 = Probability of taking action a from state s



formula8
= Given any state s and a, the probability of each next state s'



formula9
= Expected reward given any state s, next state s, and action a



How can I re-evaluate this value function in the way that is asked?









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    0












    $begingroup$


    I'm working my way through the book Reinforcement Learning by Richar S. Sutton and Andrew G. Barto and I am stuck on the following question.



    The value of a state depends on the the values of the actions possible in that state and on how likely each action is to be taken under the current policy.
    We can think of this in terms of a small backup diagram rooted at the state and considering each possible action:



    enter image description here



    Give the equation corresponding to this intuition and diagram for the value at the root node
    formula2, in terms of the value at the expected leaf node,
    formula, given
    formula3. This expectation depends on the policy,
    formula4. Then give a second equation in which the expected value is written out explicitly in terms of
    formula5such that no expected value notation appears in the equation.



    I should mention that...



    formula7
    ...



    Where...



    formula6 = Probability of taking action a from state s



    formula8
    = Given any state s and a, the probability of each next state s'



    formula9
    = Expected reward given any state s, next state s, and action a



    How can I re-evaluate this value function in the way that is asked?









    share







    New contributor




    Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      0












      0








      0





      $begingroup$


      I'm working my way through the book Reinforcement Learning by Richar S. Sutton and Andrew G. Barto and I am stuck on the following question.



      The value of a state depends on the the values of the actions possible in that state and on how likely each action is to be taken under the current policy.
      We can think of this in terms of a small backup diagram rooted at the state and considering each possible action:



      enter image description here



      Give the equation corresponding to this intuition and diagram for the value at the root node
      formula2, in terms of the value at the expected leaf node,
      formula, given
      formula3. This expectation depends on the policy,
      formula4. Then give a second equation in which the expected value is written out explicitly in terms of
      formula5such that no expected value notation appears in the equation.



      I should mention that...



      formula7
      ...



      Where...



      formula6 = Probability of taking action a from state s



      formula8
      = Given any state s and a, the probability of each next state s'



      formula9
      = Expected reward given any state s, next state s, and action a



      How can I re-evaluate this value function in the way that is asked?









      share







      New contributor




      Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I'm working my way through the book Reinforcement Learning by Richar S. Sutton and Andrew G. Barto and I am stuck on the following question.



      The value of a state depends on the the values of the actions possible in that state and on how likely each action is to be taken under the current policy.
      We can think of this in terms of a small backup diagram rooted at the state and considering each possible action:



      enter image description here



      Give the equation corresponding to this intuition and diagram for the value at the root node
      formula2, in terms of the value at the expected leaf node,
      formula, given
      formula3. This expectation depends on the policy,
      formula4. Then give a second equation in which the expected value is written out explicitly in terms of
      formula5such that no expected value notation appears in the equation.



      I should mention that...



      formula7
      ...



      Where...



      formula6 = Probability of taking action a from state s



      formula8
      = Given any state s and a, the probability of each next state s'



      formula9
      = Expected reward given any state s, next state s, and action a



      How can I re-evaluate this value function in the way that is asked?







      reinforcement-learning markov-process monte-carlo





      share







      New contributor




      Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.










      share







      New contributor




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      Check out our Code of Conduct.








      share



      share






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      Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      asked 3 mins ago









      BolboaBolboa

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      Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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