First of all, AIXI isn't actually "the optimal time bounded AI". What AIXI is "optimal" for is coming to correct conclusions when given the smallest amount of data, and by "optimal" it means "no other program does better than AIXI in at least one possible world without also doing worse in another".

Furthermore AIXI itself uses Solomonoff induction directly, and Solomonoff induction is uncomputable. (It can be approximated, though.)

AIXItl is the time-limited version if AIXI, but it amounts to "test all the programs that you can, find the best one, and use that" - and it's only "optimal" when compared against the programs that it can test, so it's not actually practical to use, either.

(At least, that's what I could gather from reading the PDF of the paper on AIXI. Could someone who knows what they're talking about correct any mistakes?)