A Theory of Universal Artificial Intelligence based on Algorithmic Complexity

TL;DR

This work constructs a unified theory of universal artificial intelligence by merging Solomonoff-style universal induction with sequential decision theory. It introduces the parameter-free AIξ model, which replaces unknown environment priors with a universal semimeasure, and proves its universality and convergence properties, at least in inductive settings. To address uncomputability, it also develops time-bounded variants (AIξ^{ ilde{t} ilde{l}}) and outlines the main theorem that such systems can be effectively as intelligent as any bounded competitor, given reasonable resource bounds. The paper further demonstrates how AIξ subsumes sequence prediction, strategic games, function minimization, and supervised learning, while highlighting horizon selection and the need for computable approximations. The resulting framework reframes intelligence as a formally solvable, albeit computationally challenging, objective across a broad class of AI tasks, with clear directions for future proofs and practical implementations.

Abstract

Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline for a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning, how the AIXI model can formally solve them. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXI-tl, which is still effectively more intelligent than any other time t and space l bounded agent. The computation time of AIXI-tl is of the order tx2^l. Other discussed topics are formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.