# How does uniform offset tiling work with function approximation?

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. 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?

• @ quest ions, did you find an answer to this problem? I have the same question. Apr 10 at 11:19
• @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 Apr 15 at 18:05

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: 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.

• Thanks! I realised this but hadn't gotten round to answer the question but you've done so here Apr 15 at 18:04