I think that's the question, unless there are some shorter or in some way better computable approximations to AIXI out there. I am not as familiar with this field as I would like, so someone please correct me if I'm making a silly mistake somewhere.
If anyone has gone to the trouble of actually counting the number of bits in AIXItl (in some particular, simple programming language / UTM), that would be nice to quote.
One variant somebody actually implemented is called Monte Carlo AIXI; granted that it won't have been optimized for minimum code size, but a Google search might find you a copy of the code you could download and look at its size for an upper bound.
Does anyone happen to know the Komogorov complexity (in some suitable, standard UTM -- or, failing that, in lines of Python or something) of computable approximations of AIXI?
I'm writing a paper on how simple or complicated intelligence is, and what implications that has for AI forecasting. In that context: adopt Shane Legg's measure of intelligence (i.e., let "intelligence" measure a system's average goal-achievement across the different "universe" programs that might be causing it to win or not win reward at each time step, weighted according to the universe program's simplicity).
Let k(x, y) denote the Kolmogorov complexity of the shortest program that attains an intelligence of at least x, when allowed an amount y of computation (i.e., of steps it gets to run our canonical UTM). Then, granting certain caveats, AIXI and approximations thereto tell us that the limit as y approaches infinity of k(x,y) is pretty small for any computably attainable value of x. (Right?)
What I'd like is to stick an actual number, or at least an upper bound, on "pretty small".
If someone could help me out, I'd be much obliged.