## Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic ProbabilityThis book presents sequential decision theory from a novel algorithmic information theory perspective. While the former is suited for active agents in known environments, the latter is suited for passive prediction in unknown environments. The book introduces these two different ideas and removes the limitations by unifying them to one parameter-free theory of an optimal reinforcement learning agent embedded in an unknown environment. Most AI problems can easily be formulated within this theory, reducing the conceptual problems to pure computational ones. Considered problem classes include sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations to other approaches. One intention of this book is to excite a broader AI audience about abstract algorithmic information theory concepts, and conversely to inform theorists about exciting applications to AI. |

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### Contents

A Short Tour Through the Book | 1 |

Simplicity Uncertainty | 29 |

2 Prefix coding of natural numbers and strings | 34 |

14 Kolmogorovs axioms of probability theory | 42 |

25 Posterior convergence of M to i | 48 |

31 MartinL6f random sequences | 54 |

Universal Sequence Prediction | 65 |

8 Convergence of random sequences | 71 |

1 The agent model | 126 |

The Universal Algorithmic Agent AIXI | 141 |

12 We expect AIXI to be universally optimal | 146 |

30 Discounted AIp model and value | 159 |

Important Environmental Classes | 185 |

Computational Aspects | 209 |

1 The fastest algorithm | 211 |

8 Effective intelligence order relation | 226 |

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