Is the derivation of REINFORCE wrong?
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In Reinforcement Learning (2nd edition) by Sutton and Barto, the REINFORCE update is derived as follows:
However, I am wondering why you can perform the transition from the second to third line, as both the first factor $G_t$ and the second factor are functions of the same random variables, $A_t$ and $S_t$ (sampled values), which are not necessarily independent. The expectation of two functions of random variables should only be reducible to the product of their expectations if the random variables are independent.
machine-learning reinforcement-learning policy-gradients
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minchminch
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In Reinforcement Learning (2nd edition) by Sutton and Barto, the REINFORCE update is derived as follows:
However, I am wondering why you can perform the transition from the second to third line, as both the first factor $G_t$ and the second factor are functions of the same random variables, $A_t$ and $S_t$ (sampled values), which are not necessarily independent. The expectation of two functions of random variables should only be reducible to the product of their expectations if the random variables are independent.
machine-learning reinforcement-learning policy-gradients
asked 11 mins ago
minchminch
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
In Reinforcement Learning (2nd edition) by Sutton and Barto, the REINFORCE update is derived as follows:
However, I am wondering why you can perform the transition from the second to third line, as both the first factor $G_t$ and the second factor are functions of the same random variables, $A_t$ and $S_t$ (sampled values), which are not necessarily independent. The expectation of two functions of random variables should only be reducible to the product of their expectations if the random variables are independent.
machine-learning reinforcement-learning policy-gradients
asked 11 mins ago
minchminch
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
In Reinforcement Learning (2nd edition) by Sutton and Barto, the REINFORCE update is derived as follows:
However, I am wondering why you can perform the transition from the second to third line, as both the first factor $G_t$ and the second factor are functions of the same random variables, $A_t$ and $S_t$ (sampled values), which are not necessarily independent. The expectation of two functions of random variables should only be reducible to the product of their expectations if the random variables are independent.
machine-learning reinforcement-learning policy-gradients
machine-learning reinforcement-learning policy-gradients
asked 11 mins ago
minchminch
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 11 mins ago
minchminch
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 11 mins ago
minchminch
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 11 mins ago
minchminch
1
asked 11 mins ago
minchminch
1
1
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
minch is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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