Now now, it doesn't require infinite resources -- the AIXItl variant of AIXI only requires an insanely massive amount of resources, more than would be feasible in the physical universe, but not an infinite amount ;-)
I think this sort of mathematical theory of intelligence is useful in helping to clarify some of the conceptual foundations of the theory of general intelligence and its relationship to computation theory. However, there is an awful lot that it can't answer, and among this mass is the question of how to create reasonable levels of general intelligence using feasible amounts of computational resources (like the ones available in the actual physical universe of which we know). -- Ben G On Nov 7, 2007 10:53 PM, Vladimir Nesov <[EMAIL PROTECTED]> wrote: > Edward, > > I think the point of Legg's and Hutter's work is in describing > completely defined solution. So far they only have a completely > defined solution which requires infinite resources. It can probably be > generalized somewhere, for example Hutter shows that prior can be > selected rather arbitrarily without giving up too much, so probably > there's a class of feasible models that can be described in a similar > framework. > > On 11/8/07, Edward W. Porter <[EMAIL PROTECTED]> wrote: > > > > > > > > HOW VALUABLE IS SOLMONONOFF INDUCTION FOR REAL WORLD AGI? > > > > Through some AGIRI links I stumbled on the Shane Legg's "Friendly AI is > > bunk" page. I was impressed. I read more of his related web pages and > > became very impressed. > > > > Then I read his paper "Solmononoff Induction." > > (http://www.vetta.org/documents/disSol.pdf ) > > > > It left me confused. I don't have a sufficient math background to > > understand all its notation, so I know I may well be wrong (I mean > totally > > wrong), but to me Solmononoff Induction, as described in the paper > seemed to > > be missing something big, at least if it were to be used for a general > > purpose AGI that was to learn from perception in the real world. > > > > I understand the basic idea that if you are seeking a prior likelihood > for > > the occurrence of an event and you have no data about the frequency of > its > > occurrence -- absent any other knowledge -- some notion of the > complexity, > > in information-theory terms, of the event might help you make a better > > guess. This makes sense because reality is a big computer, and > complexity > > -- in terms of the number of combined events required to make reality > cough > > up a given event , and the complexity of the space in which those events > are > > to be combined -- should to some extent be related to the event's > > probability. I can understand how such complexity could be approximated > by > > the length of code required in some a theoretical Universal computer to > > model such real world event-occurrence complexity. > > > > But it seems to me there are factors other than the complexity of > > representing or computing a match against a hypothesis that -- in the > an > > AGI sensing and acting in a real world -- might be much more important > and > > functional for estimating probabilities. > > > > For example, although humans are not good at accurately estimating > certain > > types of probabilities, we have an innate ability to guess probabilities > in > > a context sensitive way and by using knowledge about similar yet > different > > things. (As shown in the example quoted below from the Kemp paper > below.) > > It would seem to me that the complexity of the computation required to > > understand what is the appropriate context is not, itself, necessarily > > related to the complexity of an event occurring in that context once the > > context has been determined. > > > > Similarly, it does not seem to me that the complexity of determining > what is > > similar to what, in which ways, for purpose of determining the extent to > > which probabilities from something similar might provide an appropriate > > prior for something never-before-seen, are not necessarily related to > the > > probability of the thing never-before-seen occurring, itself. For > example, > > the complexity of perception is not directly related to the complexity > of > > occurrence. For example, complexity of perception can be greatly > affected > > by changes in light, shape, and view which might not have anything to do > > with the probability or complexity of occurrence. > > > > So what I am saying is, for example, that if you are receiving a > sequence of > > bytes from a video camera, much of the complexity in the input stream > might > > not be related to complexity-of-event-creation- or Occam's-razor-type > > issues, but rather to complexity of perception, or similarity > understanding, > > or of appropriate context selection, factors which are not themselves > > necessarily related to complexity of occurrence. > > > > Furthermore, I am saying that for an AGI it seems to me it would make > much > > more sense to attempt to derive priors from notions of similarity, of > > probabilities of similar things, events, and contexts, and from things > like > > causal models for similar or generalized classes. There is usually much > > from reality that we do know that we can, and do, use when learning > about > > things we don't know. > > > > A very good paper on this subject is one by Charles Kemp et al., > "Learning > > overhypotheses with hierarchical Bayesian models" at > > http://www.mit.edu/~perfors/KempPTDevSci.pdf<http://www.mit.edu/%7Eperfors/KempPTDevSci.pdf> > > It give a > > very good example of the power of this type of reasoning -- power that > it > > appears to me Solomonoff Induction totally lacks > > > > > > "participants were asked to imagine that they were exploring an island > in > > the Southeastern Pacific, that they had encountered a single member of > the > > Barratos tribe, and that this tribesman was brown and obese. Based on > this > > single example, participants concluded that most Barratos were brown, > but > > gave a much lower estimate of the proportion of obese Barratos (Figure > 4). > > When asked to justify their responses, participants often said that > > tribespeople were homogeneous with respect to color but heterogeneous > with > > respect to body weight (Nisbett et al., 1983)." > > > > Perhaps I am totally missing something, which is very possible, and if > so, I > > would like to have it pointed out to me, but I think the type of > > overhypothesis reasoning described in this Kemp paper is a much more > > powerful and useful source for deriving priors to be used in Bayesian > > reasoning in AGIs that are expected to learn in the "real world" than > > Solomonoff Induction. > > > > Since I expect Shane Legg is much more knowledgable than I am on the > > subject, I am expecting to be told that I am really off track, either by > him > > or someone else on this list. > > > > If so, please inform me how. > > > > Ed Porter > > 24 String Bridge S12 > > Exeter, NH 03833 > > (617) 494-1722 > > Fax (617) 494-1822 > > [EMAIL PROTECTED] ________________________________ > > This list is sponsored by AGIRI: http://www.agiri.org/email > > To unsubscribe or change your options, please go to: > > http://v2.listbox.com/member/?&; > > > -- > Vladimir Nesov mailto:[EMAIL PROTECTED] > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?&; > ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=62802349-df6493
