A universal prior assigns probability to programs that generate sequences or environments, giving exponentially greater weight to shorter descriptions. It offers a principled alternative to choosing an ad hoc prior over hypotheses. section 9.1.2 section 9.1.3
For prediction, programs that fit the observed bits gain weight and those that do not lose weight. A Bayes mixture combines their next-bit predictions, with each program contributing according to its weight. section 9.1.2
Predicting a bit stream
For an unknown stream of coin-flip-like bits, candidate programs might describe a fair coin, a biased coin, or a repeating pattern. As bits arrive, their predictive records change how much each program contributes to the next-bit prediction. section 9.1.2
AIXI uses the same prior over computable environments to choose actions that maximize expected future reward. This makes the prior part of an idealized, Bayes-optimal agent—not a practical recipe, since AIXI is incomputable and assumes unbounded resources. section 9.1.3
