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- Order Information
- Abstract
- Short Table of Contents
- Reviews at AIJ, ACM, Amazon
- MAGIC Discussion Group
- AIXI in 1 Line
- Slides
- Prizes
- Solutions to Problems
- Approximations & Implementations & Applications
- The Meanings of AIXI
- BibTeX Entry

Subtitle: Sequential Decisions based on Algorithmic Probability

Publisher: Springer, ISBN: 3-540-22139-5, DOI: 10.1007/b138233

Date: © 2005, Pages: 300

The book can be ordered from springer.com, or amazon.com, or amazon.de, or most other bookshops.

The book introduces these two well-known but very different ideas and removes the limitations by unifying them to one parameter-free theory of an optimal reinforcement learning agent embedded in an arbitrary unknown environment. Most if not all AI problems can easily be formulated within this theory, which reduces 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 to AI.

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.

- A Short Tour through the Book
- Simplicity & Uncertainty
- Universal Sequence Prediction
- Agents in Known Probabilistic Environments
- The Universal Algorithmic Agent AIXI
- Important Environmental Classes
- Computational Aspects
- Discussion

AIXI is an agent that interacts with an environment in cycles

The expression shows that AIXI tries to maximize its total future reward

One can fix any finite action and percept space, any reasonable

Various problems at the end of most chapters of the book contain open problems, where the author is not aware of any solution. Some problems represent mathematically rigorous questions to solve. In other problems the task is to make the verbal descriptions or definitions or ideas itself mathematically rigorous. Though the monetary reward is not high, it hopefully serves as an additional motivation (of course you keep the intellectual property). For determined students these problems may also be a way toward active research.

100 Euro are offered for the construction of a universal semimeasure with posterior convergence individually for all Martin-Löf random sequences. Universal may be defined in either of the following ways:

(a) dominating all enumerable semimeasures Eq.(2.27),

(b) being Solomonoff's

(c) being Levin's mixture ξ

100 Euro are offered for showing a lower bound for

100 Euro are offered for a positive or negative solution for

100 Euro for a positive solution for general computable selection rules.

50 Euro

100-500 Euro. This is one of the core open questions regarding AIXI. Proving non-asymptotic value bounds or related optimality properties. Prize depends on achieved progress in this question.

100 Euro

- Problem 2.6 has been solved (2005, by Chernov and myself)
- The Solutions to Problems 2.5 and 2.6u and 2.7u have been TeXed (2005, by myself)

- A simple Markov approximation of AIXI playing Repeated Matrix Games
- A powerful Monte Carlo CTW AIXI approximation that learns to play Poker, Pacman, TicTacToe, ...
- Web-demo of AIXI and related algorithms on Grid Worlds (by John Aslanides et al.)

- AIXI stands for Artificial Intelligence (AI) based on Solomonoff's distribution ξ (Greek letter Xi)
- AIXI stands for Artificial Intelligence (AI) crossed (X) with Induction (I)
- AIXI stands for action
*a*and percept_{i}*x*in cycle_{i}≡o_{i}r_{i}*i*(see above) - AIXI is a Catalan word (així) meaning 'in this way' or 'like that' (and with some liberties 'this is it!')
- AIXI is Pinyin romanization (àixī,àixí) of Chinese 愛惜 meaning 'to cherish/treasure' (thanks to Yuxi)
- Pronunciation: aiksi [Latin] IPA: ['aiksiː]

@Book{Hutter:04uaibook, author = "Marcus Hutter", title = "Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability", publisher = "Springer", address = "Berlin", year = "2005", isbn = "3-540-22139-5", isbn-online = "978-3-540-26877-2", pages = "300 pages", doi = "10.1007/b138233", url = "http://www.hutter1.net/ai/uaibook.htm", keywords = "Artificial intelligence; algorithmic probability; sequential decision theory; Solomonoff induction; Kolmogorov complexity; Bayes mixture distributions; reinforcement learning; universal sequence prediction; tight loss and error bounds; Levin search; strategic games; function minimization; supervised learning.", abstract = "This book presents sequential decision theory from a novel algorithmic information theory perspective. While the former theory is suited for active agents in known environments, the latter is suited for passive prediction of unknown environments. The book introduces these two well-known but very different ideas and removes the limitations by unifying them to one parameter-free theory of an optimal reinforcement learning agent interacting with an arbitrary unknown world. Most if not all AI problems can easily be formulated within this theory, which reduces the conceptual problems to pure computational ones. Considered problem classes include sequence prediction, strategic games, function minimization, reinforcement and supervised learning. Formal definitions of intelligence order relations, the horizon problem and relations to other approaches to AI are discussed. 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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