Didn't see this at the time, sorry.

So... I'm sorry if this reply seems a little unhelpful, and I wish there was some way to engage more strongly, but...

Point (1) is the main problem. AIXI updates freely over a gigantic range of sensory predictors with no specified ontology - it's a sum over a huge set of programs, and we, the users, have no idea what the representations are talking about, except that at the end of their computations they predict, "You will see a sensory 1 (or a sensory 0)." (In my preferred formalism, the program puts a probability on a 0 instead.) Inside, the program could've been modeling the universe in terms of atoms, quarks, quantum fields, cellular automata, giant moving paperclips, slave agents scurrying around... we, the programmers, have no idea how AIXI is modeling the world and producing its predictions, and indeed, the final prediction could be a sum over many different representations.

This means that equation (20) in Hutter is written as a utility function over sense data, where the reward channel is just a special case of sense data. We can easily adapt this equation to talk about any function computed directly over sense data - we can get AIXI to optimize any aspect of its sense data that we please. We can't get it to optimize a quality of the external universe. One of the challenges I listed in my FAI Open Problems talk, and one of the problems I intend to talk about in my FAI Open Problems sequence, is to take the first nontrivial steps toward adapting this formalism - to e.g. take an equivalent of AIXI in a really simple universe, with a really simple goal, something along the lines of a Life universe and a goal of making gliders, and specify something given unlimited computing power which would behave like it had that goal, without pre-fixing the ontology of the causal representation to that of the real universe, i.e., you want something that can range freely over ontologies in its predictive algorithms, but which still behaves like it's maximizing an outside thing like gliders instead of a sensory channel like the reward channel. This is an unsolved problem!

We haven't even got to the part where it's difficult to say in formal terms how to interpret what a human says s/he wants the AI to plan, and where failures of phrasing of that utility function can also cause a superhuman intelligence to kill you. We haven't even got to the huge buried FAI problem inside the word "optimal" in point (1), which is the really difficult part in the whole thing. Because so far we're dealing with a formalism that can't even represent a purpose of the type you're looking for - it can only optimize over sense data, and this is not a coincidental fact, but rather a deep problem which the AIXI formalism deliberately avoided.

(2) sounds like you think an AI with an alien, superhuman planning algorithm can tell humans what to do without ever thinking consequentialistically about which different statements will result in human understanding or misunderstanding. Anna says that I need to work harder on not assuming other people are thinking silly things, but even so, when I look at this, it's hard not to imagine that you're modeling AIXI as a sort of spirit containing thoughts, whose thoughts could be exposed to the outside with a simple exposure-function. It's not unthinkable that a non-self-modifying superhuman planning Oracle could be developed with the further constraint that its thoughts are human-interpretable, or can be translated for human use without any algorithms that reason internally about what humans understand, but this would at the least be hard. And with AIXI it would be impossible, because AIXI's model of the world ranges over literally all possible ontologies and representations, and its plans are naked motor outputs.

Similar remarks apply to interpreting and answering "What will be its effect on _?" It turns out that getting an AI to understand human language is a very hard problem, and it may very well be that even though talking doesn't feel like having a utility function, our brains are using consequential reasoning to do it. Certainly, when I write language, that feels like I'm being deliberate. It's also worth noting that "What is the effect on X?" really means "What are the effects I care about on X?" and that there's a large understanding-the-human's-utility-function problem here. In particular, you don't want your language for describing "effects" to partition, as the same state of described affairs, any two states which humans assign widely different utilities. Let's say there are two plans for getting my grandmother out of a burning house, one of which destroys her music collection, one of which leaves it intact. Does the AI know that music is valuable? If not, will it not describe music-destruction as an "effect" of a plan which offers to free up large amounts of computer storage by, as it turns out, overwriting everyone's music collection? If you then say that the AI should describe changes to files in general, well, should it also talk about changes to its own internal files? Every action comes with a huge number of consequences - if we hear about all of them (reality described on a level so granular that it automatically captures all utility shifts, as well as a huge number of other unimportant things) then we'll be there forever.

I wish I had something more cooperative to say in reply - it feels like I'm committing some variant of logical rudeness by this reply - but the truth is, it seems to me that AIXI isn't a good basis for the agent you want to describe; and I don't know how to describe it formally myself, either.