  Decision theory formally solves the problem of rational agents in uncertain
worlds if the true environmental probability distribution is known.
Solomonoff's theory of universal induction formally solves the problem of
sequence prediction for unknown distribution. We unify both theories and give
strong arguments that the resulting universal AIXI model behaves optimal in any
computable environment. 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 superior to any other time t and space l bounded agent.
The computation time of AIXI^tl is of the order t x 2^l.
