Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements
The founding definition. A problem solver may rewrite any part of its own code, including the part that searches for rewrites, once it has proved the rewrite is useful. Three later systems on this list take its name.
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Self-rewriting is gated on a proof of utility rather than on a measured improvement.
The proof requirement is what every later system replaces with an empirical test.
Abstract
We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problem-dependent 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 self-rewrite. We show that such a self-rewrite 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 self-rewrites. Unlike previous non-self-referential 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 speed-ups is provable at all.