Abstract:
We present the first class of mathematically rigorous, general, fully
selfreferential, selfimproving, optimally efficient problem solvers.
Inspired by Kurt Gödel's celebrated selfreferential formulas (1931),
a Gödel machine (or `Goedel machine' but not `Godel machine')
rewrites any part of its own code as soon
as it has found a proof that the rewrite is useful, where the
problemdependent utility function and the hardware and the entire
initial code are described by axioms encoded in an initial proof
searcher which is also part of the initial code. The searcher
systematically and efficiently tests
computable proof techniques (programs whose outputs are proofs)
until it finds a provably useful, computable selfrewrite. We show
that such a selfrewrite is
globally optimal  no local maxima!
 since the code first had to prove that it is not useful to continue the
proof search for alternative selfrewrites. Unlike previous
nonselfreferential methods based on hardwired proof searchers, ours
not only boasts an optimal order of complexity but can optimally
reduce any slowdowns hidden by the O()notation, provided the utility
of such speedups is provable at all. (FAQ)
Gödel machine papers:
9.
B. R. Steunebrink, J. Schmidhuber. Towards an Actual Gödel Machine Implementation. In P. Wang, B. Goertzel, eds.,
Theoretical Foundations of Artificial General Intelligence.
Springer, 2012.
PDF.
8.
B. Steunebrink, J. Schmidhuber.
A Family of Gödel Machine Implementations.
In Proc. Fourth Conference on Artificial General Intelligence (AGI11),
Google, Mountain View, California, 2011.
PDF.
7.
J. Schmidhuber.
Ultimate Cognition à la Gödel.
Cognitive Computation 1(2):177193, 2009. PDF.
(Springer.)
6.
J. Schmidhuber.
Completely SelfReferential Optimal Reinforcement Learners.
In W. Duch et al. (Eds.):
Proc. Intl. Conf. on Artificial Neural Networks ICANN'05,
LNCS 3697, pp. 223233, SpringerVerlag Berlin Heidelberg, 2005
(plenary talk).
PDF.
5.
J. Schmidhuber.
Gödel machines:
Fully SelfReferential Optimal Universal SelfImprovers.
In B. Goertzel and C. Pennachin, eds.: Artificial
General Intelligence, p. 119226, 2006.
PDF.
4. J. Schmidhuber.
A Technical Justification of Consciousness.
9th annual meeting of the Association for the
Scientific Study of Consciousness ASSC,
Caltech, Pasadena, CA, 2005.
3. J. Schmidhuber. Goedel machines:
Towards a Technical Justification of Consciousness.
In D. Kudenko, D. Kazakov, and E. Alonso, eds.:
Adaptive Agents and MultiAgent Systems III
LNCS 3394, p. 123, Springer, 2005.
PDF.
2.
Section on Goedel machines on page 235 of: J. Schmidhuber,
OOPS,
Machine Learning, 54, 211254, 2004.
PDF.
(The editors also offered to publish the entire original Goedel machine
paper instead of the OOPS paper, but
the latter came first chronologically).
1.
arXiv: cs.LO/0309048
(2003, revised Dec 2006)
