Proof subtracting baseline doesn't influence gradient can be used to show no gradient exist at all?












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I am using David Silver's course in RL to help me write my thesis. However, I am baffled by the proof given in lecture 7 slide 29:
slideshow



Consider in this proof replacing $b(s)$ with the critic's quality estimate $Q_w(s,a)$ (see previous slide(s)). How does this proof not also show that the gradient of the objective function $nabla_theta J(theta)$ should also be $0$? Does this have to do with the second summation term changing from being over $a$ to over $a in mathcal{A}$?



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    $begingroup$


    I am using David Silver's course in RL to help me write my thesis. However, I am baffled by the proof given in lecture 7 slide 29:
    slideshow



    Consider in this proof replacing $b(s)$ with the critic's quality estimate $Q_w(s,a)$ (see previous slide(s)). How does this proof not also show that the gradient of the objective function $nabla_theta J(theta)$ should also be $0$? Does this have to do with the second summation term changing from being over $a$ to over $a in mathcal{A}$?



    Thank you.









    share







    New contributor




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







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      $begingroup$


      I am using David Silver's course in RL to help me write my thesis. However, I am baffled by the proof given in lecture 7 slide 29:
      slideshow



      Consider in this proof replacing $b(s)$ with the critic's quality estimate $Q_w(s,a)$ (see previous slide(s)). How does this proof not also show that the gradient of the objective function $nabla_theta J(theta)$ should also be $0$? Does this have to do with the second summation term changing from being over $a$ to over $a in mathcal{A}$?



      Thank you.









      share







      New contributor




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







      $endgroup$




      I am using David Silver's course in RL to help me write my thesis. However, I am baffled by the proof given in lecture 7 slide 29:
      slideshow



      Consider in this proof replacing $b(s)$ with the critic's quality estimate $Q_w(s,a)$ (see previous slide(s)). How does this proof not also show that the gradient of the objective function $nabla_theta J(theta)$ should also be $0$? Does this have to do with the second summation term changing from being over $a$ to over $a in mathcal{A}$?



      Thank you.







      reinforcement-learning policy-gradients actor-critic





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