Towards a universal theory of artificial intelligence based on algorithmic probability and sequential decision theory

Abstract

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\textasciicircumtl, which is still superior to any other time t and space l bounded agent. The computation time of AIXI\textasciicircumtl is of the order t x 2\textasciicircuml.