"there is some number of colors k for which it is NP-hard (that is, effectively impossible) to distinguish between networks in which it is possible to satisfy at least 99% of the constraints and networks in which it is possible to satisfy at most 1% of the constraints". I think this sentence is concerning for those interested in the possibility of creating FAI.
Not really. This sounds very similar to an argument I've heard that misuses Rice's theorem to conclude that creating a provably friendly AI is impossible. Here's the argument, as I remember it: "By Rice's theorem, there is no general method for determining whether any given AI is an FAI. Therefore it is impossible to build an AI that you can prove is an FAI." The first step of the argument is correct. However, the next step does not follow; just because there is no method that can correctly tell you which of all possible AIs is friendly, it does not follow that there does not exist a method to prove that some particular AI is friendly. You could use the exact same argument to "prove" that there is no program that provably halts; after all, there is no general method for determining whether an arbitrary program halts. But of course writing a program that provably halts is actually quite easy.
I looks to me like your argument makes the same error, but starting from this graph coloring thing that I don't know anything about, instead of from Rice's theorem. The problem of classifying networks based on how many of some set of constraints it is possible for it to satisfy may be NP-hard, but that does not mean that it is difficult to find some network in which you can satisfy most or even all of the constraints.
It is possible that I'm misunderstanding your argument, but even if I am, I'm not particularly worried that it could be a real problem. You don't give a concrete reason to believe that this coloring problem has much to do with FAI. In particular, how does it relate to FAI in a way that it doesn't relate to an operating system? Operating systems are also programs that we want to satisfy a complicated set of constraints. But we can make those.
I think my reply to Lurker, above, might clarify some things. To answer your question.
Making an operating system is easy. Deciding which operating system should be used is harder. This is true despite the fact that an operating system's performance on most criteria can easily be assessed. Assessing whether an operating system is fast is easier than assessing whether a universe is "just", for example. Also, choosing one operating system from a set of preexisting options is much easier than choosing one future from all possibilities that can be cre...
I am not a computer scientist and do not know much about complexity theory. However, it's a field that interests me, so I occasionally browse some articles on the subject. I was brought to https://www.simonsfoundation.org/mathematics-and-physical-science/approximately-hard-the-unique-games-conjecture/ by a link on Scott Aaronson's blog, and read the article to reacquaint myself with the Unique Games Conjecture, which I had partially forgotten about. If you are not familiar with the UGC, that article will explain it to you better than I can.
One phrase in the article stuck out to me: "there is some number of colors k for which it is NP-hard (that is, effectively impossible) to distinguish between networks in which it is possible to satisfy at least 99% of the constraints and networks in which it is possible to satisfy at most 1% of the constraints". I think this sentence is concerning for those interested in the possibility of creating FAI.
It is impossible to perfectly satisfy human values, as matter and energy are limited, and so will be the capabilities of even an enormously powerful AI. Thus, in trying to maximize human happiness, we are dealing with a problem that's essentially isomorphic to the UGC's coloring problem. Additionally, our values themselves are ill-formed. Human values are numerous, ambiguous, even contradictory. Given the complexities of human value systems, I think it's safe to say we're dealing with a particularly nasty variation of the problem, worse than what computer scientists studying it have dealt with.
Not all specific instances of complex optimization problems are subject to the UGC and thus NP hard, of course. So this does not in itself mean that building an FAI is impossible. Also, even if maximizing human values is NP hard (or maximizing the probability of maximizing human values, or maximizing the probability of maximizing the probability of human values) we can still assess a machine's code and actions heuristically. However, even the best heuristics are limited, as the UGC itself demonstrates. At bottom, all heuristics must rely on inflexible assumptions of some sort.
Minor edits.