Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements

TL;DR

This paper introduces a mathematically rigorous class of self-referential problem solvers that can optimally improve themselves by rewriting their code based on provable utility, ensuring globally optimal self-improvement.

Contribution

It presents the first formal framework for self-referential, self-improving problem solvers with provable optimality and efficiency, inspired by Gödel's self-referential formulas.

Findings

Self-referential problem solvers can rewrite their code upon proof of usefulness.

Such solvers achieve globally optimal self-improvement without local maxima.

The approach guarantees optimal complexity and provable speed-ups.

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.