Artificial intelligence and Solomonoff induction: what to read?

Olle Häggström, Professor of Mathematical Statistics at Chalmers University of Technology, reads some of Marcus Hutter's work, comes away unimpressed, and asks for recommendations.

One concept that is sometimes claimed to be of central importance in contemporary AGI research is the so-called AIXI formalism. [...] In the presentation, Hutter advices us to consult his book Universal Artificial Intelligence. Before embarking on that, however, I decided to try one of the two papers that he also directs us to in the presentation, namely his A philosophical treatise of universal induction, coauthored with Samuel Rathmanner and published in the journal Entropy in 2011. After reading the paper, I have moved the reading of Hutter's book far down my list of priorities, because gerneralizing from the paper leads me to suspect that the book is not so good.

I find the paper bad. There is nothing wrong with the ambition - to sketch various approaches to induction from Epicurus and onwards, and to try to argue how it all culminates in the concept of Solomonoff induction. There is much to agree with in the paper, such as the untenability of relying on uniform priors and the limited interest of the so-called No Free Lunch Theorems (points I've actually made myself in a different setting). The authors' emphasis on the difficulty of defending induction without resorting to circularity (see the well-known anti-induction joke for a drastic illustration) is laudable. And it's a nice perspective to view Solomonoff's prior as a kind of compromise between Epicurus and Ockham, but does this particular point need to be made in quite so many words? Judging from the style of the paper, the word "philosophical" in the title seems to mean something like "characterized by lack of rigor and general verbosity".4 Here are some examples of my more specific complaints [...]

I still consider it plausible to think that Kolmogorov complexity and Solomonoff induction are relavant to AGI7 (as well as to statistical inference and the theory of science), but the experience of reading Uncertainty & Induction in AGI and A philosophical treatise of universal induction strongly suggests that Hutter's writings are not the place for me to go in order to learn more about this. But where, then? Can the readers of this blog offer any advice?