Interesting, if I understand correctly the idea is to find a theoretically correct basis for deciding on a course of action given existing knowledge and then to make this calculation efficient and then direct towards a formally defined objective.
Yes, but there is only one top-level objective, to do the right thing, so one doesn't need to define an objective separately from the goal system itself (and improving state of knowledge is just another thing one can do to accomplish the goal, so again not a separate issue).
FAI really stands for a method of efficient production of goodness, as we would want it produced, and there are many landmines on this path, in particular humanity in its current form doesn't seem to be able to retain its optimization goal in the long run, and the same applies to most obvious hacks that don't have explicit notions of preference, such as upload societies. It's not just a question of speed, but also of ability to retain the original goal after quadrillions of incompletely understood self-modifications.
Ok, so how about this work around.
The current approach is to have a number of human intelligences continue to explore this problem until they enter a mental state C (for convinced they have the answer to FAI). The next stage is to implement it.
We have no other route to knowledge other than to use our internal sense of being convinced. I.e. no oracle to tell us if we are right or not.
So what if we formally define what this mental state C consists of and then construct a GAI which provably pursues only the objective of creating this state. The advantage bein...
This post enumerates texts that I consider (potentially) useful training for making progress on Friendly AI/decision theory/metaethics.
Rationality and Friendly AI
Eliezer Yudkowsky's sequences and this blog can provide solid introduction to the problem statement of Friendly AI, giving concepts useful for understanding motivation for the problem, and disarming endless failure modes that people often fall into when trying to consider the problem.
For a shorter introduction, see
Decision theory
The following book introduces an approach to decision theory that seems to be closer to what's needed for FAI than the traditional treatments in philosophy or game theory:
Another (more technical) treatment of decision theory from the same cluster of ideas:
Following posts on Less Wrong present ideas relevant to this development of decision theory:
Mathematics
The most relevant tool for thinking about FAI seems to be mathematics, where it teaches to work with precise ideas (in particular, mathematical logic). Starting from a rusty technical background, the following reading list is one way to start:
[Edit Nov 2011: I no longer endorse scope/emphasis, gaps between entries, and some specific entries on this list.]