No, there's no particular reason to think an FAI would be better at learning than an UFAI analogue, at least not as far as I can see.
However, one of the problems needed to be solved for FAI (stable self-modification) could certainly make an FAI's rate of self-improvement faster than a comparative AI which has not solved that problem. There are other questions that need to be answered there (does the AI realize that modifications will go wrong and therefore not self-modify? If it's smart enough to notice the problem, won't it's first step be to solve it?), and I may be off base here.
I'm not sure it's that useful to talk about an FAI vs a analogue UFAI, though. If an FAI is built, there will be many significant differences between the resulting intelligence and the one that would have been built if the FAI was not, simply due to the different designers. In terms of functioning, the different design choices, even those not relevant to FAI (if that's even meaningful - FAI may well need to be so fully integrated that all the aspects are made with it in mind), may be radically different depending on the designer and are likely to have most of the effect you're talking about.
In other words, we don't know shit about what the first AGI might look like, and we certainly don't know enough to do detailed separate counterfactuals
No, there's no particular reason to think an FAI would be better at learning than an UFAI analogue, at least not as far as I can see.
I believe you have this backwards - the OP is asking whether a FAI would be worse at learning than an UFAI, because of additional constraints on its improvement. If so:
then a non Friendly AI would eventually (possibly quite quickly) become smarter than any FAI built.
Of course one of the first actions of a FAI would be to prevent any UFAI from being built at all.
Haven't had one of these for awhile. This thread is for questions or comments that you've felt silly about not knowing/understanding. Let's try to exchange info that seems obvious, knowing that due to the illusion of transparency it really isn't so obvious!