> it doesn't believe it can affect it's own brain in any way I think this is the biggest problem with AIXI. Whilst we can argue whether an existing AIXI would

> it doesn't believe it can affect it's own brain in any way I think this is the biggest problem with AIXI. Whilst we can argue whether an existing AIXI would have properties X, Y, Z, that's kind of irrelevant because AIXI can't exist (it's incomputable). The real point of AIXI is to help researchers by defining something to use in models or to compare their work against. Unfortunately, as you say, its algorithm is fixed. What we'd really like is for AIXI to be the fixed-point or limit of some iterative/recursive process; then, even though a true AIXI is unrealisable, we could still kick off the process and push it as far as we can. In fact, AIXI is actually the limiting case of AIXI(t, l), which is an AIXI-like algorithm whose Turing machine models halt after t steps or using l tape cells (whichever comes first). AIXI is the limit as t and l approach infinity. This isn't particularly helpful though, as it just tells AI researchers that making bigger, faster computers will help, which we already knew. In that sense, Schmidhuber's Goedel Machine architecture is potentially more fruitful. Last I saw, there was no real implementation yet ( e.g. http://people.idsia.ch/~juergen/selfreflection.pdf‎ http://people.idsia.ch/~juergen/selfreflection.pdf‎ ). The Powerplay architecture is more easily realisable, as it optimises greedily rather than optimally, and uses regression tests rather than a verification. In fact, we can also make another architecture in between these two, which optimises greedily but uses verification instead of regression tests. I've implemented this in Coq at http://chriswarbo.net/essays/powerplay http://chriswarbo.net/essays/powerplay