For an extensive list of prerequisite texts, see Marcus Hutter’s (perhaps overwhelming) reading list available under “Books & Courses” at his personal website.
Assuming undergraduate level math background, a good place to start is the recent textbook “An Introduction to Universal Artificial Intelligence” by Marcus Hutter, Elliot Catt, and David Quarel.
For a deeper background on algorithmic information theory (AIT), the canonical source is “An Introduction to Kolmogorov Complexity and its Applications” by Ming Li and Paul Vitanyi.
There is ongoing lively discussion of AIXI at the online forum lesswrong, see an overview at https://www.lesswrong.com/w/aixi
Even if you feel that you are still building the necessary background, feel free to reach out to an organizer (e.g. colewyeth@gmail.com) for guidance.
Introductory Papers
Universal Algorithmic Intelligence: A Mathematical Top->Down Approach
An early introduction to AIXI and AIXItl, summarizing in paper form many of the ideas from the textbook “Universal Artificial Intelligence.”
A Philosophical Treatise of Universal Induction
A good introduction to the philosophical problems addressed (and solved?) by Solomonoff induction.
Tom Sterkenberg’s Thesis: Universal Prediction
An unusually strong and well-researched rebuttal to optimality and other common claims about Solomonoff induction from a mathematical philosopher. Also includes very clear and careful definitions and some nice results. A longer read but worth (critically) engaging with.
Jan Leike’s Thesis: Nonparametric General Reinforcement Learning
A collection of major technical improvements to the theory of UAI, particularly computability results, negative convergence results, and an AIT solution to the longstanding grain of truth problem from economics. Some of Leike’s results still seem to be near the research frontier.
A Monte Carlo AIXI Approximation
A practical “AIXI approximation.” The CTW belief distribution is really weaker than Solomonoff’s universal distribution, but otherwise the “implementation” is fairly direct and helps to understand the theory.
This is a deeper and still fairly rigorous and practical approximation of the universal distribution using a transformer.
Note: In principle, the last two papers can be combined to produce an AIXI approximation with a more universal belief distribution. I (Cole Wyeth) have experimented with this a bit, and it does seem possible to learn very simple games this way, but hard to compete with the original Monte Carlo AIXI approximation. But perhaps I am just not cracked enough! Giving it a try can be a nice way to understand the previous couple of papers, and is probably fairly easy for a decent SWE. Also, I have tested LLMs ability to perform Solomonoff induction in context using the program distribution sampler implemented in “Learning Universal Predictors,” with decent results; I’m not likely to follow up on this myself, but it could be an interesting benchmark! (More meaningful for base models)
ASI Safety
The AIXI framework has been applied to analyze the safety (and danger) of ASI systems, and to motivate technical plans for aligning, controlling, or minimizing the (potentially catastrophic) harms of ASI, including the first PhD thesis entirely focused on AI safety by Tom Everitt:
Towards Safe Artificial General Intelligence
I also recommend Michael K. Cohen’s blog:
For a brief summary of the literature, see Marcus Hutter’s recent talk:
https://www.youtube.com/watch?v=qHqv3GvWBTM
For a condensed argument for and explanation of extinction risk from ASI (yes, this is much more serious than today’s problems e.g. political bias or sycophancy), see Yudkowsky and Soares’ new book:
If Anyone Builds It, Everyone Dies
Universal Algorithmic Intelligence 