Self-Improving Artificial Intelligence: Achieving Optimal Performance Through Self-Reference and Universal Problem Solving

Title: Self-Improving Artificial Intelligence: Achieving Optimal Performance Through Self-Reference and Universal Problem Solving

Abstract: This research explores the concept of self-improving artificial intelligence (AI) by proposing a self-referential universal problem solver. The proposed model, known as a Gödel machine, is designed to solve arbitrary computational problems in an optimal fashion. It incorporates an axiomatic description of its hardware, problem-specific utility function, environment, computational costs, and initial software. The machine also includes a sub-optimal initial problem-solving policy and an asymptotically optimal proof searcher. Unlike previous approaches, the Gödel machine can rewrite any part of its software, including axioms and proof searcher, as soon as it finds a proof that will improve its future performance. The research demonstrates that these self-rewrites are globally optimal, ensuring that no alternative rewrites or proofs are worth waiting for.

Introduction: The dream of computer scientists is to build an optimally efficient universal problem solver. This research proposes a self-referential universal problem solver, called a Gödel machine, which can achieve optimal performance in solving arbitrary computational problems. The machine's initial software includes an axiomatic description of its hardware, problem-specific utility function, environment, computational costs, and initial software itself. It also includes a sub-optimal initial problem-solving policy and an asymptotically optimal proof searcher.

The Gödel machine's unique feature is its ability to rewrite any part of its software, including axioms and proof searcher, to improve its future performance. This self-improvement strategy is globally optimal, ensuring that no alternative rewrites or proofs are worth waiting for.

Results: The research presents a formal details of a particular Gödel machine, including an overview of its hardware and initial software, and a description of how online proof techniques connect syntax and semantics. It also discusses bias-optimal proof search (Biops), which the initial proof searcher uses to solve the first proof search task. The research demonstrates that Biops ensures asymptotic optimality despite online proof generation.

Discussion: The Gödel machine can exhibit various types of self-improvements, such as changes in its hardware, software, and problem-solving policies. The research presents example applications of the Gödel machine, including probabilistic hardware and limitations of the machine. It also discusses relations to previous work on self-improving machines and practical issues.

Conclusion: In conclusion, the proposed Gödel machine is a self-referential universal problem solver that can achieve optimal performance in solving arbitrary computational problems. The machine's ability to rewrite any part of its software to improve its future performance ensures that it is globally optimal. The research opens up new possibilities for self-improving AI and universal problem solving.

Link to Article: https://arxiv.org/abs/0309048v3 Authors: arXiv ID: 0309048v3