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

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 distributions. We unify both theories and give strong arguments that the resulting universal AIξ model behaves optimally in any computable environment. The major drawback of the AIξ model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIξtl, which is still superior to any other time t and length l bounded agent. The computation time of AIξtl is of the order t·2l.