The Solomonoff expectation value of any unbounded computable utility function diverges. This is because the program “produce the first universe with utility > n^2” is roughly of length log n + O(1) therefore it contributes 2^{-log n + O(1)} n^2 = O(n) to the expectation value.
The Solomonoff expectation value of any unbounded computable utility function diverges. This is because the program “produce the first universe with utility > n^2” is roughly of length log n + O(1) therefore it contributes 2^{-log n + O(1)} n^2 = O(n) to the expectation value.