Is there another non-trivial mathematical account of how an agent can come to have accurate knowledge of its environment
Pretty much: Solomonoff Induction. That does most of the work in AIXI. OK, it won't design experiments for you, but there are various approaches to doing that...
When I use the word 'AIXI' above, I mean to include Solomonoff induction. I would have thought that was obvious.
One has to learn Solomonoff induction to learn AIXI.
I searched the posts but didn't find a great deal of relevant information. Has anyone taken a serious crack at it, preferably someone who would like to share their thoughts? Is the material worthwhile? Are there any dubious portions or any sections one might want to avoid reading (either due to bad ideas or for time saving reasons)? I'm considering investing a chunk of time into investigating Legg's work so any feedback would be much appreciated, and it seems likely that there might be others who would like some perspective on it as well.