Is a finite Solomonoff learner worse than human learning?
Your suppositions are wrong.  A finite Solomonoff learner can learn the all-1's string.  There does exist a learning algorithm that can output a program for the all-1's string.

Consequently, this example does not demonstrate that Solomonoff learners are necessarily worse than a human being.  They might be; but this example doesn't prove that.

For instance, consider the following learning algorithm: if the inputs is all-1's, then output a program that only outputs 1's (e.g., 10001011 in your example), otherwise do something arbitrary.  This is a trivial algorithm, but it demonstrates that there does exist a learning algorithm that can learn that sequence.  In other words, you've given an example of an input sequence that both a human can learn and a finite Solomonoff learner can learn.

What you might have shown is that if we restrict the learner to a very limited amount of memory, then the learner might not be able to learn some things that a human can.  But that's a rather uninteresting conclusion.  Of course we know that if you severely restrict the memory of the computer, that limits what it can compute.  For instance, if we limit the memory of the algorithm to only 7 bits, then the algorithm must act like a finite-state machine with at most 128 states, which severely limits the patterns it can find.  A human can learn sequences that can't be recognized by a finite-state machine with 128 states.  That's not surprising, and doesn't really have any interesting implications for whether finite Solomonoff learners are worse than human learning.

There's no point in comparing a human to a computer algorithm that has been massively handicapped.  To make the comparison interesting, you must allow the computer algorithm to have reasonable access to the resources that any computer would have; otherwise you have trivialized the question.  This means allowing the computer learner a non-trivial amount of memory.  And once you do that, the learner no longer has any difficulties with your sequence.



There are other issues in your post.  If you are assuming that the only possible approach is to try all possible algorithms until you find one that works, that's not the case.  More seriously, the problem of "given a sequence, find the elegant program for it" is not computable, so if you require the learner to find the shortest possible program, you've created an impossible problem.  Finally, where you say that "According to Kolmogorov complexity, the length of the elegant program is independent of the Turing machine implementation.", but that's not correct.  What is true is that changing the universal Turing machine will change the length by only a constant... but if you care about constants, that might be important.