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I get the fundamental idea of how tilings work, but, in Barton and Sutton's book, Reinforcement Learning: An Introduction (2nd edition), a diagram, on page 219 (figure 9.11), showing the variations of uniform offset tiling has confused me.

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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?

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  • $\begingroup$ @ quest ions, did you find an answer to this problem? I have the same question. $\endgroup$
    – DSPinfinity
    Commented Apr 10, 2022 at 11:19
  • $\begingroup$ @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 $\endgroup$
    – quest ions
    Commented Apr 15, 2022 at 18:05

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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

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.

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  • $\begingroup$ Thanks! I realised this but hadn't gotten round to answer the question but you've done so here $\endgroup$
    – quest ions
    Commented Apr 15, 2022 at 18:04

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