Universal Artificial Intelligence : Sequential Decisions Based on Algorithmic Probability
This 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 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.
Algorithmic information theory : Mathematics of digital information processing
This book treats the Mathematics of many important areas in digital information processing.It covers, in a unified presentation, five topics: Data Compression, Cryptography, Sampling (Signal Theory), Error Control Codes, Data Reduction. The thematic choices are practice-oriented. So, the important final part of the book deals with the Discrete Cosine Transform and the Discrete Wavelet Transform, acting in image compression. The presentation is dense, the examples and numerous exercises are concrete. The pedagogic architecture follows increasing mathematical complexity.

