Should I model a problem with quantised output as classification or regression?

Say I have some data I am trying to learn, and I'm aware that the output is quantised in some way, e.g. I can get only get discrete values (0.1, 0.2, 0.3...0.9) in a finite range.

Would you treat that as regression or classification? In this case the numbers do have a relation to each other e.g. 0.3 is close to 0.4 in meaning.

I could treat it as classification with a softmax final layer with N outputs, or could treat it as regression with a linear layer with single output and then somehow quantise the result post-prediction. But my gut feeling is that the fact there is a finite number of answers that that should somehow be used in my model?

1. Treat it as a normal regressor where you clip the output to your range, and then define thresholds arbitrarily, such as $$.36 \rightarrow .4$$, $$.34 \rightarrow .3$$, etc..