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Yvain comments on The Domain of Your Utility Function - Less Wrong
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Comments (94)
I don't think this post adequately distinguishes between two concepts: how does the human utility function actually work, and how should it work.
The answer to the first question is (I thought people here agreed) that humans weren't actually utility maximizers; this makes things like your descriptive argument against perceptive determinism unnecessary and a lot of your wording misleading.
The second question is: if we're making some artificial utility function for an AI or just to prove a philosophical point, how should that work - and I think your answer is spot on. I would hope that people don't really disagree with you here and are just getting bogged down by confusion about real brains and some map-territory distinctions and importing epistemology where it's not really necessary.
Agreed. This post seems to add little to the discourse. However, it's useful to write clear, concise posts to sum these things up from time to time. With pictures!
Where I've seen people use PDUs in AI or philosophy, they weren't confused, but rather chose to make the assumption of perception-determined utility functions (or even more restrictive assumptions) in order to prove some theorems. See these examples:
Here's a non-example, where the author managed to prove theorems without the PDU assumption:
I wrote earlier:
Well, here's a recent SIAI paper that uses perception-determined utility functions, but apparently not in order to prove theorems (since the paper contains no theorems). The author was advised by Peter de Blanc, who two years ago wrote the OP arguing against PDUs. Which makes me confused: does the author (Daniel Dewey) really think that PDUs are a good idea, and does Peter now agree?
I don't think that human values are well described by a PDU. I remember Daniel talking about a hidden reward tape at one point, but I guess that didn't make it into this paper.
An adult agent has access to its internal state and its perceptions. If we model its access to its internal state as via internal sensors, then sense data are all it has access too - its only way of knowing about the world outside of its genetic heritage.
In that case, utility functions can only accept sense data as inputs - since that is the only thing that any agent ever has access to.
If you have a world-determined utility function, then - at some stage - the state of the world would first need to be reconstructed from perceptions before the function could be applied. That makes the world-determined utility functions an agent can calculate into a subset of perception-determined ones.
Spot on for what, precisely? If one's goal is to make an AI that mirrors human values, it would not be every useful for it to use an utterly alien model of thought like utility maximization. ISTM that superhuman AI is the one place where you can't afford to use wishful thinking models in place of understanding what humans really do, and how they'll really act.
To model how humans really work, the AI needs to study real humans, not be a real human. The best bridge engineers are not themselves bridges.
(Maybe I completely misunderstood what you wrote, in which case please correct me, but it looks like you're suggesting that AIs that mirror human values must be implemented in the way humans really work.)
I'm saying that a system that's based on utility maximizing is likely too alien of a creature to be able to be safely understood and utilized by humans.
That's more or less the premise of FAI, is it not? Any strictly-maximizing agent is bloody dangerous to anything that isn't maximizing the same thing. What's more, humans are ill-equipped to even grok this danger, let alone handle it safely.
The best bridges are not humans either.
Utility maximization can model any goal-oriented creature, within reason. Familiar, or alien, it makes not the slightest bit of difference to the theory.
Of course it can, just like you can model any computation with a Turing machine, or on top of the game of Life. And modeling humans (or most any living entity) as a utility maximizer is on a par with writing a spreadsheet program to run on a Turing machine. An interesting, perhaps fun or educational but exercise, but mostly futile.
I mean, sure, you could say that utility equals "minimum global error of all control systems", but it's rather ludicrous to expect this calculation to predict their actual behavior, since most of their "interests" operate independently. Why go to all the trouble to write a complex utility function when an error function is so much simpler and closer to the territory?
I think you are getting my position. Just as a universal computer can model any other type of machine, so a utilitiarian agent can model any other type of agent. These two concepts are closely analogous.
But your choice of platforms is not without efficiency and complexity costs, since maximizers inherently "blow up" more than satisficers.
I think humans can be accurately modelled as expected utility maximizers - provided the utility function is allowed to access partial recursive functions.
The agents you can't so model have things like uncomputable utility functions - and we don't needed to bother much about those.
People who claim humans are not expected utility maximizers usually seem to be making a much weaker claim: humans are irrational, human's don't optimise economic or fitness-based utility functions - or something like that - not that there exists no utility function that could possibly express their actions in terms of their sense history and state.
PCT and Ainslie actually propose that humans are more like disutility minimizers and appetite satisficers. While you can abuse the notion of "utility" to cover these things, it leads to wrong ideas about how humans work, because the map has to be folded oddly to cover the territory.
Utility as a technical term in decision theory isn't equivalent to happiness and disutility isn't equivalent to unhappiness. Rather, the idea is to find some behaviorally descriptive function which takes things like negative affectivity and appetite satisfaction levels as arguments and return a summary, which for lack of a better term we call utility. The existence of such a function is required by certain axioms of consistency -- the thought is that if one's behavior cannot be described by a utility function, then they will have intransitive preferences.
As a descriptive statement, human beings probably do have circular preferences; the prescriptive question is whether there is a legitimate utility function we can extrapolate from that mess without discarding too much.
You inevitably draw specific actions, so there is no escaping forming a preference over actions (a decision procedure, not necessarily preference over things that won't play), and "discarding too much" can't be an argument against the inevitable. (Not that I particularly espouse the form of preference being utility+prior.)
Sorry, I meant something like "whether there is a relatively simple decision algorithm with consistent preferences that we can extrapolate from that mess without discarding too much". If not, then a superintelligence might be able to extrapolate us, but until then we'll be stymied in our attempts to think rationally about large unfamiliar decisions.
Fair enough. Note that the superintelligence itself must be a simple decision algorithm for it to be knowably good, if that's at all possible (at the outset, before starting to process the particular data from observations), which kinda defeats the purpose of your statement. :-)
Well, the code for the seed should be pretty simple, at least. But I don't see how that defeats the purpose of my statement; it may be that short of enlisting a superintelligence to help, all current attempts to approximate and extrapolate human preferences in a consistent fashion (e.g. explicit ethical or political theories) might be too crude to have any chance of success (by the standard of actual human preferences) in novel scenarios. I don't believe this will be the case, but it's a possibility worth keeping an eye on.
Oh, indeed. I just want to distinguish between things that humans really experience and the technical meaning of the term "utility". In particular, I wanted to avoid a conversation in which disutility, which sounds like a euphemism for discomfort, is juxtaposed with decision theoretic utility.
Nitpick: if one's behavior cannot be described by a utility function, then one will have preferences that are intransitive, incomplete, or violate continuity.
I'm with you on "incomplete" (thanks for the catch!) but I'm not so sure about "violate continuity". Can you give an example of preferences that are transitive and complete but violate continuity and are therefore not encodable in a utility function?
Lexicographic preferences are the standard example: they are complete and transitive but violate continuity, and are therefore not encodable in a standard utility function (i.e. if the utility function is required to be real-valued; I confess I don't know enough about surreals/hyperreals etc. to know whether they will allow a representation).
I'd heard that mentioned before around these parts, but I didn't recall it because I don't really understand it. I think I must be making a false assumption, because I'm thinking of lexicographic ordering as the ordering of words in a dictionary, and the function that maps words to their ordinal position in the list ought to qualify. Maybe the assumption I'm missing is a countably infinite alphabet? English lacks that.
The wikipedia entry on lexicographic preferences isn't great, but gives the basic flavour:
That entry says,
So my intuition above was not correct -- an uncountably infinite alphabet is what's required.
Intransitive preferences don't mean that you can't describe an agent's actions with a utitilty function. So what if an agent prefers A to B, B to C and C to A? It might mean they will drive in circles and waste their energy - but it doesn't mean you can't describe their preferences with a utility function. All it means is that their utility function will not be as simple as it could be.
In the standard definition, the domain of the utility function is the set of states of the world and the range is the set of real numbers; the preferences among states of the world are encoded as inequalities in the utility of those states. I read your comment as asserting that there exists real numbers a, b, c, such that a > b, b > c, and c > a. I conclude that you must have something other than the standard definition in mind.
If A is Alaska, B is Boston, and C is California, the preferences involve preferring being in Alaska if you are in Boston, preferring being in Boston if you are in California, and preferring being in California if you are in Alaska. The act of expressing those preferences using a utility function does not imply any false statements about the set of real numbers.
Preferring A to B means that, given the choice between A and B, you will pick A, regardless of where you currently are (you might be in California but have to leave). This is not the same thing as choosing A over B, contingent on being in B.
You can indeed express the latter set of preferences you describe using a standard utility function, but that's because you've redefined them so that they're no longer intransitive.
Its not clear you're contradicting Cyan. You describe the converse of what he describes.
Even if a utility function can be written down which allows intransitive preferences, its worth noting that transitive preferences is a standard assumption.
ISTM that if an agent's preferences cannot be described by a utility function, then it is because the agent is either spatially or temporally infinite - or because it is uncomputable.
I'm struggling to see how such a utility function could work. Could you give an example of a utility function that describes the preferences you just set out, and has the implication that u(x)>u(y) <=> xPy?
It’s not difficult to code (if A:B,if B:C,if C:A) into a utilitarian system. If A is Alaska, B is Boston, and C is California, that would cause driving in circles.
With respect, that doesn't seem to meet my request. Like Cyan, I'm tempted to conclude that you are using a non-standard definition of "utility function".
ETA: Oh, wait... perhaps I've misunderstood you. Are you trying to say that you can represent these preferences with a function that assigns: u(A:B)>u(x:B) for x in {B,C}; u(B:C)>u(x:C) for x in {A,C} etc? If so, then you're right that you can encode these preferences into a utility function; but you've done so by redefining things such that the preferences no longer violate transitivity; so Cyan's original point stands.
Cyan claimed some agent's behaviour corresponded to intransitive preferences. My example is the one that is most frequently given as an example of circular preferences. If this doesn't qualify, then what behaviour are we talking about?
What is this behaviour pattern that supposedly can't be represented by a utility function due to intransitive preferences?
Suppose I am in Alaska. If told I can either stay or go to Boston, I choose to stay. If told I can either stay or go to California, I choose California. If told I must leave for either Boston or California, I choose Boston. These preferences are intransitive, and AFAICT, cannot be represented by a utility function. To do so would require u(A:A)>u(B:A)>u(C:A)>u(A:A).
More generally, it is true that one can often redefine states of the world such that apparently intransitive preferences can be rendered transitive, and thus amenable to a utility representation. Whether it's wise or useful to do so will depend on the context.
Utility maximisation is not really a theory about how humans work. AFAIK, nobody thinks that humans have an internal representation of utility which they strive to maximise. Those that entertain this idea are usually busy constructing a straw-man critique.
It is like how you can model catching a ball with PDEs. You can build a pretty good model like that - even though it bears little relationship to the actual internal operation.
[2011 edit: hmm - the mind actually works a lot more like that than I previously thought!]
That's kind of ironic that you mention PDE's, since PCT actually proposes that we do use something very like an evolutionary algorithm to satisfice our multi-goal controller setups. IOW, I don't think it's quite accurate to say that PDE's "bear little relationship to the actual internal operation."
I thought so too even as recently as a month ago, but Post Your Utility Function and If it looks like utility maximizer and quacks like utility maximizer... for pretty strong arguments against this.
The arguments in the posts themselves seem unimpressive to me in this context. If there are strong arguments that human actions cannot, in principle, be modelled well by using a utility function, perhaps they should be made explicit.
Agreed. Now, if it were possible to write a complete utility function for some person, it would be pretty clear that "utility" did not equal happiness, or anything simple like that.
I tend to think that the best candidate in most organisms is "expected fitness". It's probably reasonable to expect fairly heavy correlations with reward systems in brains - if the organisms have brains.
Agents which can't be modelled by a utility-based framework are:
AFAIK, there's no good evidence that either kind of agent can actually exist. Counter-arguments are welcome, of course.
Do you have models which explain economics which don't involve individual utility maximization and yet do as well or better. I'm not saying that models of utility maximization are always best, social scientists, including economists, are discovering this But I do think expected utility maximization is currently the best approach to a large class of problems.
I'm pretty sure that the first reasonably-intelligent machines will work much as illustrated in the first diagram - for engineering reasons: it is so much easier to build them that way. Most animals are wired up that way too - as we can see from their drug-taking behaviour.