In the spirit of AIXItl but more practical, see Juergen's new work on the
"Goedel Machine" AGI architecture

http://www.idsia.ch/~juergen/goedelmachine.html

I don't think this is really a practical AGI architecture, but I think it's
really interesting ... I do like the direction this research program is
moving in...

"
Abstract of 2003 paper: A Goedel machine solves general computational
problems in a possibly stochastic and reactive environment. Its initial
software includes an axiomatic description of (1) the Goedel machine's
hardware, (2) known aspects of the environment, (3) goals and rewards to be
achieved, (4) costs of actions and computations, (5) the initial software
itself (no circularity involved here). It also includes a possibly
sub-optimal initial problem-solving policy and a proof searcher searching
the space of computable proof techniques, that is, programs whose outputs
are proofs. Unlike previous approaches, the self-referential Goedel machine
will rewrite any part of its software (including axioms and proof searcher)
as soon as it has found a proof that this will improve its future
performance. By definition, it produces optimal self-improvements, given
arbitrary formalized problems and typically limited computational resources;
its optimality notion is not restricted to the concept of asymptotic
optimality. To initialize the proof searcher we may use the recent Optimal
Ordered Problem Solver (OOPS).
"

My problem with this approach is that automated theorem-proving is very
hard!  Current AI systems cannot prove nontrivial theorems without human
intervention at crucial decision points.  I'm guessing that OOPS also has
this property.  The theorems that the Goedel machine must prove in order to
do its self-improvement are not simple ones.

A related complaint is that it may not be optimal to self-modify only when a
provable improvement is found.  It may be optimal to self-modify when a
probabilistically-likely-to-be-helpful improvement is found, based on
heuristic estimates that don't constitute a formal proof.  Now, if this is
the case, eventually a Goedel machine will discover this and modify itself
to make appropriate heuristic probability estimates.  But how will it get to
this point, if it lacks the ability to control its inferences well enough to
do complex proofs???  ;-)


-- Ben



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