What's the size of the space NM is searching for this plan?
Well that really depends on how you count things....
One way to calculate it would be to look at the number of trees with <15
nodes, with say 20 possibilities at each node.
Because in practice the plans it comes up with, with the current
parameter settings used in that experiment, are going
to be of that form.
But there are syntactic restrictions on the trees it will form, and we
haven't calculated the number of possible trees
obeying the syntactic restrictions.
And of course NM is not *guaranteed* to only formulate plans obeying
these size restrictions -- that's just probabilistically
what happens with these parameter settings. So if run long enough it
would search a much larger space, but slowly...
Anyway: As I noted in a prior response, it's obvious that a simple
reinforcement learning algorithm could learn the same behavior
shown here. In the main, getting NM to learn to play fetch using
probabilistic logic was an exercise in system
integration; the logic engine on its own has done more interesting
things than that before...
If you rewarded it for, say, regularities in arithmetic, starting with set
theory, how long would it take it to come up with, say, Goldbach's
conjecture?
We were doing that kind of "unsupervised pattern mining" experiment in
2004, using BOA Programming (the predecessor
of our current MOSES probabilistic evolutionary learning algorithm), but
not that exact experiment. Haven't played with
that sort of stuff for a while, though.
At this stage, that kind of experiment would still be best approached
using, for instance, MOSES all on its own, or MOSES+PLN
integrated in a purpose-specific way. It wouldn't really benefit from
the integrative NM architecture as a whole, in the latter's
current form.. Ultimately it would of course, though, once the
integrative architecture is more mature.
I don't know how long MOSES or MOSES+PLN would take to come up with
Goldbach's Conjecture, but I'm sure that it would
do so, along with a lot of other stuff.
But that sort of pattern mining doesn't involve the same sort of
challenges as integrated perception/action/cognition in a sim
world. E.g. it doesn't require that you deal with time at all, in
reasoning nor in pragmatic resource allocation, etc.
-- Ben
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