The Theory of Universal Computation: Bayesian Optimality, Solomonoff Induction & AIXI

A mathematical formulation of universal artificial intelligence, known as AIXI, is presented as an attempt to create a perfect induction machine. The framework begins with foundational concepts like probability axioms and Bayesian inference, which governs how to update beliefs with new evidence. To address the challenge of assigning prior probabilities in Bayesian models, the content introduces algorithmic information theory and Kolmogorov complexity. The Solomonoff prior, or universal prior, is then explained as the bridge between these concepts, providing the necessary structure for the AIXI formalism which integrates sequential decision theory and Occam's Razor.