Universal Problem Solvers Making: Provably Optimal Self-Improvements

Title: Universal Problem Solvers Making: Provably Optimal Self-Improvements

Abstract: This research proposes a self-referential universal problem solver called a G¨odel machine. It is designed to solve general computational problems in a possibly stochastic and reactive environment. The G¨odel machine's initial software includes an axiomatic description of the machine's hardware, known aspects of the environment, goals and rewards, computational costs, and the initial problem-solving policy. It also includes a proof searcher that searches for computable proof techniques. Unlike previous approaches, the self-referential G¨odel machine rewrites any part of its software as soon as it finds a proof that will improve its future performance. This approach ensures optimal self-improvements, given arbitrary formalized problems and typically limited computational resources. The research discusses the machine's hardware, initial software, proof searcher, and self-improvement strategy, demonstrating its bias-optimal proof search (BIOPS) and its ability to solve proof search tasks asymptotically optimally. The research also highlights the potential applications of the G¨odel machine, its limitations, relations to previous work, and practical issues.

Main Research Question: Can we develop a self-referential universal problem solver that can solve general computational problems in a possibly stochastic and reactive environment, and improve its performance over time by rewriting any part of its software?

Methodology: The research uses a combination of mathematical logic, computer science, and artificial intelligence to develop the G¨odel machine. It employs axiomatic systems, proof techniques, and online problem-solving methods to create a self-improving machine that can solve problems in a dynamic environment.

Results: The research presents a detailed description of the G¨odel machine, including its hardware, initial software, proof searcher, and self-improvement strategy. It demonstrates that the machine can solve proof search tasks asymptotically optimally and produce provably optimal self-improvements.

Implications: The G¨odel machine presents a novel approach to problem-solving and self-improvement in artificial intelligence. It has the potential to revolutionize the field by providing a universal problem solver that can adapt and improve its performance over time. This could lead to significant advancements in various applications, such as autonomous robotics, natural language processing, and game-playing algorithms.

Conclusion: In conclusion, the research has successfully proposed a self-referential universal problem solver called the G¨odel machine. It has demonstrated that the machine can solve general computational problems in a dynamic environment and improve its performance over time by rewriting any part of its software. The research highlights the potential applications and implications of the G¨odel machine, and future work will focus on implementing and testing the machine in various real-world scenarios.

Link to Article: https://arxiv.org/abs/0309048v1 Authors: arXiv ID: 0309048v1