Answers.Body: <p>In this particular diagram, they are showing:</p>
  <ul>
  <li>For a given state (shown by the small <span class="math-container">$+$</span> symbol), which tiles in each of the 8 tilings this state belongs to.</li>
  </ul>
  <p>So the only difference between the cells in this diagram is the state the <span class="math-container">$+$</span> is from.</p>
  <p>Following this, they show:</p>
  <p><a href="https://i.sstatic.net/kYRIb.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kYRIb.png" alt="Asymmetrically Offset Tilings" /></a></p>
  <p>As such, the authors are showing how asymmetrically offset tilings tend to have less variance in how states are generalized by the tiles (in each tiling) they belong to.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-04-15T18:04:17.940Z
Answers.Text: Thanks! I realised this but hadn't gotten round to answer the question but you've done so here
Answers.UserDisplayName: quest ions
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-03-06T23:06:56.837Z
Answers.LastActivityDate: 2022-03-07T22:25:47.860Z
Answers.LastEditDate: 2022-03-07T22:25:47.860Z
Answers.UserDisplayName: ssp
Body: <p>I get the fundamental idea of how tilings work, but, in <a href="http://incompleteideas.net/book/RLbook2020.pdf#page=241" rel="nofollow noreferrer">Barton and Sutton's book, Reinforcement Learning: An Introduction (2nd edition)</a>, a diagram, on page 219 (figure 9.11), showing the variations of uniform offset tiling has confused me.</p>
  <p><a href="https://i.sstatic.net/QRYwa.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QRYwa.png" alt="enter image description here" /></a></p>
  <p>I don't understand why all 8 of these figures are instances of uniformly offset tilings. I thought uniformly offset meant ALL tilings have to be offset an equal amount from each other which is only the case for the bottom left figure. Is my understanding wrong?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-10T11:19:45.607Z
Comments.Text: @ quest ions,  did you find an answer to this problem? I have the same question.
Comments.UserDisplayName: DSPinfinity
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-04-15T18:05:28.360Z
Comments.Text: @DSPinfinity the tiles they represent here refer to the features within the tilings. The tilings are still offset uniformly but the features/tiles can have this sort of formation. If you go back two pages you can see a visualisation of this
Comments.UserDisplayName: quest ions
Tags: <reinforcement-learning><function-approximation><feature-selection><tile-coding><coarse-coding>
Title: How does uniform offset tiling work with function approximation?
UserDisplayName: quest ions
ThreadText: # How does uniform offset tiling work with function approximation?
  
  (Asked by: username_0 on 2020-12-19)
  
  I get the fundamental idea of how tilings work, but, in [Barton and Sutton's book, Reinforcement Learning: An Introduction (2nd edition)](http://incompleteideas.net/book/RLbook2020.pdf#page=241), a diagram, on page 219 (figure 9.11), showing the variations of uniform offset tiling has confused me.
  
  [![enter image description here](https://i.sstatic.net/QRYwa.png)](https://i.sstatic.net/QRYwa.png)
  
  I don't understand why all 8 of these figures are instances of uniformly offset tilings. I thought uniformly offset meant ALL tilings have to be offset an equal amount from each other which is only the case for the bottom left figure. Is my understanding wrong?
  
  **Tags:** reinforcement-learning, function-approximation, feature-selection, tile-coding, coarse-coding
  
  > **Comments:**
  > **username_1**: @ username_0 username_0,  did you find an answer to this problem? I have the same question.  
  > **username_0**: @username_1 the tiles they represent here refer to the features within the tilings. The tilings are still offset uniformly but the features/tiles can have this sort of formation. If you go back two pages you can see a visualisation of this  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2022-03-06. Score: 0 | Accepted answer
  
  In this particular diagram, they are showing:
  
  * For a given state (shown by the small $+$ symbol), which tiles in each of the 8 tilings this state belongs to.
  
  So the only difference between the cells in this diagram is the state the $+$ is from.
  
  Following this, they show:
  
  [![Asymmetrically Offset Tilings](https://i.sstatic.net/kYRIb.png)](https://i.sstatic.net/kYRIb.png)
  
  As such, the authors are showing how asymmetrically offset tilings tend to have less variance in how states are generalized by the tiles (in each tiling) they belong to.
  
  > **Comments:**
  > **username_0**: Thanks! I realised this but hadn't gotten round to answer the question but you've done so here  
  
  ---
  
  