Bounded utility and infinite utility are different things. A utility function u from outcomes to real numbers is bounded if there is a number M such that for every outcome x, we have |u(x)| < M.
When we talk about utility functions, we're talking about functions that encode a rational agent's preferences. It does not represent how happy an agent is.
Bounded utility and infinite utility are different things. A utility function u from outcomes to real numbers is bounded if there is a number M such that for every outcome x, we have |u(x)| < M.
I was confused, thanks There are two ways that I can imagine having a bounded utility function; either define the function so that it has a finite bound or only define it over a finite domain. I was only thinking about the former when I wrote that comment (and not assuming its range was limited to the reals, e.g. "infinity" was a valid utility), an...
I've been reading through this to get a sense of the state of the art at the moment:
http://lukeprog.com/SaveTheWorld.html
Near the bottom, when discussing safe utility functions, the discussion seems to center on analyzing human values and extracting from them some sort of clean, mathematical utility function that is universal across humans. This seems like an enormously difficult (potentially impossible) way of solving the problem, due to all the problems mentioned there.
Why shouldn't we just try to design an average bounded utility maximizer? You'd build models of all your agents (if you can't model arbitrary ordered information systems, you haven't got an AI), run them through your model of the future resulting from a choice, take the summation of their utility over time, and take the average across all the people all the time. To measure the utility (or at least approximate it), you could just ask the models. The number this spits out is the output of your utility function. It'd probably also be wise to add a reflexive consistency criteria, such that the original state of your model must consider all future states to be 'the same person.' -- and I acknowledge that that last one is going to be a bitch to formalize. When you've got this utility function, you just... maximize it.
Something like this approach seems much more robust. Even if human values are inconsistent, we still end up in a universe where most (possibly all) people are happy with their lives, and nobody gets wireheaded. Because it's bounded, you're even protected against utility monsters. Has something like this been considered? Is there an obvious reason it won't work, or would produce undesirable results?
Thanks,
Dolores