Re: Is a general purpose mechanism possible?

1. AIXI isn't computable.
AIXI based on Solomonoff's Algorithmic Probability is not computable
due to general non-computability of the halting problem. As you alude
to below, a variant measure based on time/length limited turing
machines is computable, and converges just as well.

2. AIXI tl is limited to quite small programs. If the answer is larger
than that it obviously can't find it.
Time/length limited AIXItl is not limited to quite small programs,
because t and/or l can be made arbitrarily long.

3. I don't agree that ockham's razor is always the most reasonable bias
to have. Sometimes paranoia (expecting seemingly normal people to have
a more complex motivation) is justified.
The whole point of Algorithmic Probability is to prove that occam's
razor is indeed the most reasonable bias to have for any predictive
model, all else being equal. You don't assume a more complex
motivation unless there is evidence, in which case things are no longer
equal.

4. AIXI is only guaranteed to converge on computable sequences, since a
lot of sequences in nature will be generated by processes that are more
complex than the machine (such as humans and societies of humans, the
weather), they will not be computable by AIXI. So I don't see what the
guarantee actually gets you.
The weather is not predictable, but it is most certainly computable.
Weather models would not exist otherwise. Extreme sensitivity to
initial conditions are the cause of unpredictability. To assume
computability means merely to assume that there exist laws governing
the natural world, which every scientist assumes to be true.
However, the point is well taken that the "computation" in nature will
be of greater complexity than that of the (natural or artificial)
intelligent agent WITHIN nature. However, the minimal algorithm which
reproduces a particular sequence of observations to a given accuracy
will quarantee an algorithm which exploits every possible symmetry,
invariant and pattern in the data. Otherwise, such pattern could be
exploited to produce an even smaller algorithm. The minimal algorithm
exhausts all pattern, and is itself patternless and truely random. An
algorithm that exploits every possible pattern necessarily embodies
every possible 'law of nature' applicable to the data, as the data
because large, and thus solves the induction problem in the general
sense.
Algorithmic Probability is one of the truly deep mathematical results
of this century, and the clever use of it in solving the modeling
problem in dynamic programming is genius, IMHO.

.

Relevant Pages

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