In reply to a few previous comments: AIXI and Solomonoff induction both use infinite computer power and thus clearly are not practical in any sense. AIXI(tl) is finite but not really much better as the computation time is still out of this universe. This much I think we all agree on.
Calling them "useless" however seems a bit harsh to me. For one, they can be used as theoretical models of how a super intelligence can and cannot behave. Thus, even if they don't have a practical use, they can still be useful theoretically. Currently there is nothing else that I know of that allows one to study the properties of such a powerful learning machine theoretically. Another point is that predicting the future is a risky business. There have been many areas of pure math that did not have any practical use for many many years, until somebody discovered that the math turned out to be useful for some strange thing in particle physics or something. Maybe in 20 years some really smart person will do something strange with AIXI, perhaps by modifying it in some unexpected way and all of a sudden they start to get results of large practical significance. I don't know, maybe. In any case, I wouldn't totally rule out somebody building on these ideas to do something useful in the future. I can't really see how they would do it, and the results I've proven about prediction systems place some clear constraints what is possible in this direction. Perhaps something like a totally new kind of complexity theory? In the case of Solomonoff induction, various statistical methods such as maximum likelihood, maximum entropy and minimum description length can all be derived from Solomonoff induction by approximating it in some way. Historically that's is not what happened, however the point is that if you took Solomonoff induction and tried to approximate it in various reasonable ways then you end up with genuinely practical statistical methods. Of course these new methods lose the really amazing power that Solomonoff induction has, but you couldn't claim that they are not useful. It was hoped that with AIXI something similar would be possible. So far that hasn't happened. Again, the truly amazing power of AIXI would be lost in this approximation process, however perhaps a still useful algorithm could result? Currently the best result in this direction is a simple repeated matrix playing game that is somewhat AIXIish in a limited way in this limited domain. Doing something more ambitious seems to be very difficult, but who knows, perhaps one day somebody will work something out. We will only know for sure whether AIXI theory was useful or not when we can look back 1000 years from now. Shane ----- 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/?list_id=11983
