Self-Improving, Optimally Efficient Problem Solvers: Introducing Gödel Machines

Title: Self-Improving, Optimally Efficient Problem Solvers: Introducing Gödel Machines

Abstract: This research introduces a novel class of problem solvers called Gödel machines. These machines are designed to be fully self-referential and capable of making provably optimal self-improvements. They are inspired by Kurt Gödel's self-referential formulas and operate based on a formal goal, a utility function, and an initial proof searcher, all of which are encoded within the machine. The machines systematically test computable proof techniques until they find a provably useful, computable self-rewrite. This approach ensures that the machines make globally optimal self-changes, as proven by the Global Optimality Theorem (Theorem 4.1, Section 4). The machines can also be used to create bias-optimal proof searchers, which allow the machines to solve remaining proof search tasks using the optimal order of complexity.

The research discusses the limitations of Gödel machines, provides an essential detail of one representative machine, and presents a discussion and comparison with previous work. It also explores the implications of Gödel machines in the context of human intelligence and consciousness. Overall, the research demonstrates the potential of Gödel machines as a new approach to problem-solving and machine learning, allowing for self-improving, optimally efficient systems.

Link to Article: https://arxiv.org/abs/0309048v4 Authors: arXiv ID: 0309048v4