Understanding state-value and action-value Bellman equations
$begingroup$
In Reinforcement Learning, the Bellman Optimality equations are important for defining optimal policies to be taken by a learning algorithm. The following two equations are commonly cited...
...
and
...
From a high level I understand how each work, I get that the state-value function returns the optimal policy from going from one state to another and I get that the action-value returns the optimal policy of taking an action from a particular state. What I don't understand is why these equations work out mathematically.
Why is the max function outside of the equation for the state-action function and why is it placed inside for the action-value function? I must be missing some fundamental information about how each equation works. Can someone explain the difference to me?
reinforcement-learning markov-process monte-carlo
asked 59 secs ago
BolboaBolboa
1085
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.
$endgroup$
add a comment |
$begingroup$
In Reinforcement Learning, the Bellman Optimality equations are important for defining optimal policies to be taken by a learning algorithm. The following two equations are commonly cited...
...
and
...
From a high level I understand how each work, I get that the state-value function returns the optimal policy from going from one state to another and I get that the action-value returns the optimal policy of taking an action from a particular state. What I don't understand is why these equations work out mathematically.
Why is the max function outside of the equation for the state-action function and why is it placed inside for the action-value function? I must be missing some fundamental information about how each equation works. Can someone explain the difference to me?
reinforcement-learning markov-process monte-carlo
asked 59 secs ago
BolboaBolboa
1085
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.
$endgroup$
add a comment |
$begingroup$
In Reinforcement Learning, the Bellman Optimality equations are important for defining optimal policies to be taken by a learning algorithm. The following two equations are commonly cited...
...
and
...
From a high level I understand how each work, I get that the state-value function returns the optimal policy from going from one state to another and I get that the action-value returns the optimal policy of taking an action from a particular state. What I don't understand is why these equations work out mathematically.
Why is the max function outside of the equation for the state-action function and why is it placed inside for the action-value function? I must be missing some fundamental information about how each equation works. Can someone explain the difference to me?
reinforcement-learning markov-process monte-carlo
asked 59 secs ago
BolboaBolboa
1085
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.
$endgroup$
In Reinforcement Learning, the Bellman Optimality equations are important for defining optimal policies to be taken by a learning algorithm. The following two equations are commonly cited...
...
and
...
From a high level I understand how each work, I get that the state-value function returns the optimal policy from going from one state to another and I get that the action-value returns the optimal policy of taking an action from a particular state. What I don't understand is why these equations work out mathematically.
Why is the max function outside of the equation for the state-action function and why is it placed inside for the action-value function? I must be missing some fundamental information about how each equation works. Can someone explain the difference to me?
reinforcement-learning markov-process monte-carlo
reinforcement-learning markov-process monte-carlo
asked 59 secs ago
BolboaBolboa
1085
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.
asked 59 secs ago
BolboaBolboa
1085
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.
asked 59 secs ago
BolboaBolboa
1085
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.
asked 59 secs ago
BolboaBolboa
1085
asked 59 secs ago
BolboaBolboa
1085
1085
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.
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.
Bolboa is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "557"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Bolboa is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f46563%2funderstanding-state-value-and-action-value-bellman-equations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Bolboa is a new contributor. Be nice, and check out our Code of Conduct.
Bolboa is a new contributor. Be nice, and check out our Code of Conduct.
Bolboa is a new contributor. Be nice, and check out our Code of Conduct.
Bolboa is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Data Science Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f46563%2funderstanding-state-value-and-action-value-bellman-equations%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
