Gödel Machines: Towards a Technical Justification of Consciousness [chapter]

Jürgen Schmidhuber
2005 Lecture Notes in Computer Science  
The growing literature on consciousness does not provide a formal demonstration of the usefulness of consciousness. Here we point out that the recently formulated Gödel machines may provide just such a technical justification. They are the first mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers, "conscious" or "self-aware" in the sense that their entire behavior is open to introspection, and modifiable. A Gödel machine is a computer
more » ... t rewrites any part of its own initial code as soon as it finds a proof that the rewrite is useful, where the problem-dependent utility function, the hardware, and the entire initial code are described by axioms encoded in an initial asymptotically optimal proof searcher which is also part of the initial code. This type of total self-reference is precisely the reason for the Gödel machine's optimality as a general problem solver: any 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. Optimality Theorem 1, and Section 5 an O()-optimal (Theorem 2) initial proof searcher. Section 6 provides examples and additional relations to previous work, and lists answers to several frequently asked questions about Gödel machines. Section 7 wraps up. Basic Overview / Most Relevant Previous Work / Limitations All traditional algorithms for problem solving are hardwired. Some are designed to improve some limited type of policy through experience [19], but are not part of the modifiable policy, and cannot improve themselves in a theoretically sound way. Humans are needed to create new / better problem solving algorithms and to prove their usefulness under appropriate assumptions. Here we eliminate the restrictive need for human effort in the most general way possible, leaving all the work including the proof search to a system that can rewrite and improve itself in arbitrary computable ways and in a most efficient fashion. To attack this "Grand Problem of Artificial Intelligence," we introduce a novel class of optimal, fully self-referential [10] general problem solvers called Gödel machines [43, 44] . 1 They are universal problem solving systems that interact with some (partially observable) environment and can in principle modify themselves without essential limits apart from the limits of computability. Their initial algorithm is not hardwired; it can completely rewrite itself, but only if a proof searcher embedded within the initial algorithm can first prove that the rewrite is useful, given a formalized utility function reflecting computation time and expected future success (e.g., rewards). We will see that self-rewrites due to this approach are actually globally optimal (Theorem 1, Section 4), relative to Gödel's well-known fundamental restrictions of provability [10] . These restrictions should not worry us; if there is no proof of some self-rewrite's utility, then humans cannot do much either. The initial proof searcher is O()-optimal (has an optimal order of complexity) in the sense of Theorem 2, Section 5. Unlike hardwired systems such as Hutter's [15, 16] (Section 2) and Levin's [23, 24] , however, a Gödel machine can in principle speed up any part of its initial software, including its proof searcher, to meet arbitrary formalizable notions of optimality beyond those expressible in the O()-notation. Our approach yields the first theoretically sound, fully self-referential, optimal, general problem solvers.
doi:10.1007/978-3-540-32274-0_1 fatcat:twyyq4cqmzeednza23ilvqu2tm