## Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic ProbabilityPersonal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans. |

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### Contents

Uncertainty 29 | 30 |

2 Preﬁx coding of natural numbers and strings | 34 |

14 Kolmogorovs axioms of probability theory | 41 |

25 Posterior convergence of M to p | 48 |

31 MartinL6f random sequences | 54 |

Universal Sequence Prediction | 65 |

8 Convergence of random sequences | 71 |

36 Error bound | 83 |

1 The agent model | 126 |

The Universal Algorithmic Agent AIXI | 141 |

12 We expect AIXI to be universally optimal | 146 |

30 Discounted Alp model and value | 159 |

Important Environmental Classes 185 | 184 |

Computational Aspects | 210 |

1 The fastest algorithm | 211 |

8 Effective intelligence order relation | 226 |

### Common terms and phrases

action agent AIXI model AIXItl algorithmic information theory Alp model approximable arbitrary argument assume assumption asymptotically axioms Bayes mixtures binary chain rule chronological semimeasure classiﬁcation coding conditional probabilities constant convergence countable cycle decision theory deﬁned deﬁnition depends deterministic discount enumerable semimeasures environment ergodic MDPs error bounds exists feedback ﬁnd ﬁnite ﬁnitely computable ﬁrst ﬁxed formal hence horizon implies induction inequality inﬁnite input interpreted Kolmogorov complexity Lemma length Levin search loss bounds loss functions machine learning maximize measure minimization Occam’s razor optimal policy output Pareto optimality performance player prediction scheme predictor preﬁx prior probability probabilistic probability distribution probability theory problem classes proﬁt proof prove random recursive reinforcement learning restricted reward sum satisﬁed Section self-optimizing policies sense sequence prediction Solomonoff solve speciﬁc string supervised learning Theorem true universal prior universal Turing machine weights YES YES zero