## Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements (2003)

Citations: | 16 - 7 self |

### BibTeX

@MISC{Schmidhuber03gödelmachines:,

author = {Jürgen Schmidhuber},

title = {Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements},

year = {2003}

}

### OpenURL

### Abstract

An old dream of computer scientists is to build an optimally ecient universal problem solver. We show how to solve arbitrary computational problems in an optimal fashion inspired by Kurt Gödel's celebrated self-referential formulas (1931). Our Godel machine's initial software includes an axiomatic description of: the Godel machine's hardware, the problem-speci c utility function (such as the expected future reward of a robot), known aspects of the environment, costs of actions and computations, and the initial software itself (this is possible without introducing circularity). It also includes a typically sub-optimal initial problem-solving policy and an asymptotically optimal proof searcher searching the space of computable proof techniques|that is, programs whose outputs are proofs. Unlike previous approaches, the self-referential Gödel 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, given its typically limited computational resources. We show that self-rewrites are globally optimal|no local minima!|since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for.