First of all what constitutes a useful feature?
A feature is useful if it helps to improve our play? Or: A feature is useful if it can be used in an easy calculation (linear space, time in the number of features?) to compute an optimal (or just 'good enough'??) move.
Now, about questions/answers:
If I understand well, the essential components of a question are:
- A binary valued(?) function defined over a state/state-transition,
- some policies assumed for the players,
- and some nonnegative weights (why should the weights be normalized??)
I think it is critical to say something about what policies are we allowed to choose. If there is no restriction on this set, then the `question hypothesis' can be shown to hold:
Simply choose the optimal policies for both players and ask the question:
- the binary valued function takes value 1 iff player #1 wins
- the policies are the optimal policies for both players
- the weights are all one (could use discounting, but why?)
Another question is when the binary valued function is changed to a function that takes the value of 1 iff player #2 wins
Same for draw.
Now, the answers to these questions just give us everything we need to know about the positions in order to play optimally.
These are useful features!
Hence, in order to make the `question hypothesis' more interesting, we should maybe restrict what policies we are allowed to choose in the questions.
Still, in this case, if we did choose such a policy-set then I have the feeling that the `question hypothesis' will be hard to make a non-trivial hypothesis (it either fails to easily, or can be shown to hold easily because we have so much flexibility).