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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?

nbro
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quest ions
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1 Answers1

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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.

ssp
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