What does an equal sign mean in a parenthesis? [closed]

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I'm now learning about Reinforcement Learning and in the Bellman equation, there is a following equal sign.

I understand the meaning of the left side of the equation, which is the probability of transitioning from state s to state s' with action a. However on the right side, what does the = sign mean?

The pr likely means the probability (but then why does it not use P?), and the | means given the condition of the right side, right? But I don't understand what the equal sign here means, and why is needed... IOW, what makes it different from pr(s_t+1 | s_t, a_t)?

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asked Jul 22 at 13:04

Blaszard

114115

closed as unclear what you're asking by Did, Xander Henderson, Mostafa Ayaz, José Carlos Santos, max_zorn Jul 23 at 0:05

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Learn probability first
  – GuySa
  Jul 22 at 13:06
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  By all means, do what @GuySa suggested.
  – Did
  Jul 22 at 13:32
  

  
  
  
  

add a comment | 

up vote
-1
down vote

favorite

I'm now learning about Reinforcement Learning and in the Bellman equation, there is a following equal sign.

I understand the meaning of the left side of the equation, which is the probability of transitioning from state s to state s' with action a. However on the right side, what does the = sign mean?

The pr likely means the probability (but then why does it not use P?), and the | means given the condition of the right side, right? But I don't understand what the equal sign here means, and why is needed... IOW, what makes it different from pr(s_t+1 | s_t, a_t)?

notation

share|cite|improve this question

asked Jul 22 at 13:04

Blaszard

114115

closed as unclear what you're asking by Did, Xander Henderson, Mostafa Ayaz, José Carlos Santos, max_zorn Jul 23 at 0:05

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Learn probability first
  – GuySa
  Jul 22 at 13:06
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  By all means, do what @GuySa suggested.
  – Did
  Jul 22 at 13:32
  

  
  
  
  

add a comment | 

up vote
-1
down vote

favorite

up vote
-1
down vote

favorite

I'm now learning about Reinforcement Learning and in the Bellman equation, there is a following equal sign.

I understand the meaning of the left side of the equation, which is the probability of transitioning from state s to state s' with action a. However on the right side, what does the = sign mean?

The pr likely means the probability (but then why does it not use P?), and the | means given the condition of the right side, right? But I don't understand what the equal sign here means, and why is needed... IOW, what makes it different from pr(s_t+1 | s_t, a_t)?

notation

share|cite|improve this question

asked Jul 22 at 13:04

Blaszard

114115

I'm now learning about Reinforcement Learning and in the Bellman equation, there is a following equal sign.

I understand the meaning of the left side of the equation, which is the probability of transitioning from state s to state s' with action a. However on the right side, what does the = sign mean?

The pr likely means the probability (but then why does it not use P?), and the | means given the condition of the right side, right? But I don't understand what the equal sign here means, and why is needed... IOW, what makes it different from pr(s_t+1 | s_t, a_t)?

notation

share|cite|improve this question

asked Jul 22 at 13:04

Blaszard

114115

share|cite|improve this question

share|cite|improve this question

asked Jul 22 at 13:04

Blaszard

114115

asked Jul 22 at 13:04

Blaszard

114115

asked Jul 22 at 13:04

Blaszard

114115

114115

closed as unclear what you're asking by Did, Xander Henderson, Mostafa Ayaz, José Carlos Santos, max_zorn Jul 23 at 0:05

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

closed as unclear what you're asking by Did, Xander Henderson, Mostafa Ayaz, José Carlos Santos, max_zorn Jul 23 at 0:05

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Learn probability first
  – GuySa
  Jul 22 at 13:06
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  By all means, do what @GuySa suggested.
  – Did
  Jul 22 at 13:32
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Learn probability first
  – GuySa
  Jul 22 at 13:06
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  By all means, do what @GuySa suggested.
  – Did
  Jul 22 at 13:32
  

  
  
  
  

3

3

Learn probability first
– GuySa
Jul 22 at 13:06

Learn probability first
– GuySa
Jul 22 at 13:06

1

1

By all means, do what @GuySa suggested.
– Did
Jul 22 at 13:32

By all means, do what @GuySa suggested.
– Did
Jul 22 at 13:32

add a comment | 

2 Answers
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The right hand side would be read:

"The conditional probability that $s_t+1$ is equal to $s'$ given that the value of $s_t$ is equal to $s$ and that the value of $a_t$ is equal to $a$."

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answered Jul 22 at 13:09

paw88789

28.2k12248

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up vote
1
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It means the probability that the state at time $t+1$ is $s'$ given that the state and action at time $t$ are $s$ and $a$.

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answered Jul 22 at 13:11

BDN

573417

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

The right hand side would be read:

"The conditional probability that $s_t+1$ is equal to $s'$ given that the value of $s_t$ is equal to $s$ and that the value of $a_t$ is equal to $a$."

share|cite|improve this answer

answered Jul 22 at 13:09

paw88789

28.2k12248

add a comment | 

up vote
1
down vote

The right hand side would be read:

"The conditional probability that $s_t+1$ is equal to $s'$ given that the value of $s_t$ is equal to $s$ and that the value of $a_t$ is equal to $a$."

share|cite|improve this answer

answered Jul 22 at 13:09

paw88789

28.2k12248

add a comment | 

up vote
1
down vote

up vote
1
down vote

The right hand side would be read:

"The conditional probability that $s_t+1$ is equal to $s'$ given that the value of $s_t$ is equal to $s$ and that the value of $a_t$ is equal to $a$."

share|cite|improve this answer

answered Jul 22 at 13:09

paw88789

28.2k12248

The right hand side would be read:

"The conditional probability that $s_t+1$ is equal to $s'$ given that the value of $s_t$ is equal to $s$ and that the value of $a_t$ is equal to $a$."

share|cite|improve this answer

answered Jul 22 at 13:09

paw88789

28.2k12248

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 13:09

paw88789

28.2k12248

answered Jul 22 at 13:09

paw88789

28.2k12248

answered Jul 22 at 13:09

paw88789

28.2k12248

28.2k12248

add a comment | 

add a comment | 

up vote
1
down vote

It means the probability that the state at time $t+1$ is $s'$ given that the state and action at time $t$ are $s$ and $a$.

share|cite|improve this answer

answered Jul 22 at 13:11

BDN

573417

add a comment | 

up vote
1
down vote

It means the probability that the state at time $t+1$ is $s'$ given that the state and action at time $t$ are $s$ and $a$.

share|cite|improve this answer

answered Jul 22 at 13:11

BDN

573417

add a comment | 

up vote
1
down vote

up vote
1
down vote

It means the probability that the state at time $t+1$ is $s'$ given that the state and action at time $t$ are $s$ and $a$.

share|cite|improve this answer

answered Jul 22 at 13:11

BDN

573417

It means the probability that the state at time $t+1$ is $s'$ given that the state and action at time $t$ are $s$ and $a$.

share|cite|improve this answer

answered Jul 22 at 13:11

BDN

573417

share|cite|improve this answer

share|cite|improve this answer

answered Jul 22 at 13:11

BDN

573417

answered Jul 22 at 13:11

BDN

573417

answered Jul 22 at 13:11

BDN

573417

573417

add a comment | 

add a comment |