Hi there.
I do agree with your point Robert Waite.
I have yet seen no such paper as one that would prove that there is such thing
as scalability based on any mathematical proofs.
So all your points at criticizing the "mathematical certainty" of the
scalability, is probably 100% right. There is no such things as mathematical
certainty there.
It can be modelized easily, as you already did : what if the the "evaluation
function" is giving "on purpose" wrong data. How would one mathematically prove
that it doesn't ? You would at a minimum have to know WHAT the "evaluation
function" ACTUALLY exactly is ... In fact all the evidences that we have
gathered about the scalability may rather been surprising to some persons : why
in hell does all that works so well ?
But, it's a "proven" fact that it does indeed works well so far. So that it
seems perfectly natural to speak such phrases as "there are evidences that
given the hardware we got in twenty years, human will be beaten by current
algorithms". I don't see how those evidences can be qualified with the term
"mathematical", but they are here (hiding among us !). Now if someone has the
feeling that maybe there is a roadblock, it has to be considered for what it is
: a personal intuition. What is this intuitions precisely based on ? Why are
you trying to share it with us in the first place. For myself, i believe that
what you are trying to do, is to begin to analyses all the data the community
has gathered so far, trying to understand why indeed it worked so well that it
even beaten out a pro with a 9 stones handicap and with as few as 1.7 million
evaluations/second (running on some 800 hundreds cores). To the point that the
pro felt he had no chances of wining at all with that much of a handicap. Your
are trying to understand this, and are probably right on track for that goal.
The term "mathematical" is very valuable to you, and you'll find it that it has
a much wider use (on this list) than what you would like it to. But now,
"mathematics" as proven to be of little use in the context of go programming
lately. It's more of a "physician" world. You make up a (mathematical) model.
You test it again "reality" via experimentations. You then get "empirical"
certitudes that the model is indeed correct.
There is no way of mathematically proving that light speed would still be
constant if i chose to dance naked on the champs-Elysée some day. You'll
definitely find no paper on that. Yet to speak of it as mathematically certain,
is probably not as wrong as it sound.
But as it is, i'm playing the devil advocates here. I'm totally agreeing with
you. I found your way to fight irrationnality very interesting indeed. It's
been very refreshing.
---------------------------------------------------------------------
Robert Waite has wrote :
I would really like to see what paper you are referring to. Do you mean
"Bandit based Monte-Carlo Planning"? Please post the name of the paper which
you are referring to. I do not think that the empirical evidence is
overwhelming that it is scalable in a practical way for the problem of
beating a human.
Now the topic has moved to scalable to beat a human and I disagree with the
interpretation of the data. We are both interpreting data. Your data doesn't
count as a theory.. where you reduced my theory to one that has no data. We
are both interpreting the same data. Diminishing returns was just an example
of something that could be a roadblock. I was questioning how this
necessarily scales to humans. It seems more data is needed from MC-programs
vs. humans to make a rigorous theory of scalability. So far.. the only
scalability that seems proven is a case for solving the game... not beating
humans. There is some point between that would most likely in my opinion
lead to humans being beaten.. some amount of calculation before you solved
it.. but the shape of this curve is something I am unsure of. It doesn't
seem that unreasonable to question if there is a practical scalability.
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