Shane,
Life (and especially scientific life) is all about making judgment calls.
As Ben pointed out (in what I thought was a beautifully incisive
comparison), AIXI is not unlike a system that generates The Greatest
Novel In All Of Human History by a process that involves the writing out
of all possible sequences of words .... somewhere in that collection of
word-strings is going to be The Greatest Novel In All Of Human History.
If I came along and said "There: I wrote a program that, if run on an
infinite computer for an infinite length of time, will generate
TGNIAOHH, so I have solved the general problem of writing the greatest
novel," how generous would you be with your praise?
And if I followed that with a statement that, having solved the general
problem, I am now doing some work to see how it can be repackaged into a
version that can be run on real computers, how generous would you be then?
Would you defend my claims by pointing to the many abstract, pure math
theories that were considered "useless" at first, but which later turned
out to have practical applications?
I doubt it. You would make a judgment call, and dismiss my claim about
having solved the problem of building a novel-writing system as
"useless." That's if you were being polite.
What is amazing to me is that if someone *did* make a claim about such a
novel-writing "theory", the credibility and attention they would attract
would be directly proportional to the amount of dense mathematics
contained in the theory. No math: no credibility. Huge amounts of
math that is incomprehensible to anyone except a full-time pure
mathematician: serious discussion across the world, a PhD thesis and a
prestigious position in a heavyweight center of learning. Same theory,
mind you - exactly the same actual content and claims, but just dressed
up differently.
Seen it happen before. Tired of it. Just gets in the way of real science.
No wonder no one has built an actual artificial intelligence yet.
Richard Loosemore.
Shane Legg wrote:
In reply to a few previous comments:
AIXI and Solomonoff induction both use infinite computer power
and thus clearly are not practical in any sense. AIXI(tl) is finite
but not really much better as the computation time is still out
of this universe. This much I think we all agree on.
Calling them "useless" however seems a bit harsh to me. For one,
they can be used as theoretical models of how a super intelligence
can and cannot behave. Thus, even if they don't have a practical
use, they can still be useful theoretically. Currently there is nothing
else that I know of that allows one to study the properties of such
a powerful learning machine theoretically.
Another point is that predicting the future is a risky business.
There have been many areas of pure math that did not have any
practical use for many many years, until somebody discovered
that the math turned out to be useful for some strange thing in
particle physics or something. Maybe in 20 years some really
smart person will do something strange with AIXI, perhaps by
modifying it in some unexpected way and all of a sudden they
start to get results of large practical significance.
I don't know, maybe. In any case, I wouldn't totally rule out
somebody building on these ideas to do something useful in
the future. I can't really see how they would do it, and the
results I've proven about prediction systems place some clear
constraints what is possible in this direction. Perhaps something
like a totally new kind of complexity theory?
In the case of Solomonoff induction, various statistical methods
such as maximum likelihood, maximum entropy and minimum
description length can all be derived from Solomonoff induction
by approximating it in some way. Historically that's is not what
happened, however the point is that if you took Solomonoff
induction and tried to approximate it in various reasonable ways
then you end up with genuinely practical statistical methods.
Of course these new methods lose the really amazing power that
Solomonoff induction has, but you couldn't claim that they are not
useful.
It was hoped that with AIXI something similar would be possible.
So far that hasn't happened. Again, the truly amazing power of
AIXI would be lost in this approximation process, however perhaps
a still useful algorithm could result? Currently the best result in
this direction is a simple repeated matrix playing game that is
somewhat AIXIish in a limited way in this limited domain. Doing
something more ambitious seems to be very difficult, but who
knows, perhaps one day somebody will work something out.
We will only know for sure whether AIXI theory was useful or
not when we can look back 1000 years from now.
Shane
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